### Selective branching, quenching, and converting of topological modes

A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be distinguished by their response to localized flux defects, resulting in the binding of modes whose stability can be traced back to that of convectional edge states. The reduced dimensionality of these objects renders the possibility of arranging them in distinct geometries, such as arrays that branch or terminate in the bulk. We show that the prospect of hybridizing the modes in such new kinds of channels poses profound opportunities in a dynamical context. In particular, we find that creating junctions of $\pi$-flux chains or extending them as function of time can induce transistor and stop-and-go effects. Pending controllable initial conditions certain branches of the extended defect array can be actively biased. Discussing these physical effects within a generally applicable framework that relates to a variety of established artificial topological materials, such as mass-spring setups and LC circuits, our results offer an avenue to explore and manipulate new transport effects that are rooted in the topological characterization of the underlying system.

### Flag manifold sigma models from SU($n$) chains

One dimensional SU($n$) chains with the same irreducible representation $\mathcal{R}$ at each site are considered. We determine which $\mathcal{R}$ admit low-energy mappings to a $\text{SU}(n)/[\text{U}(1)]^{n-1}$ flag manifold sigma model, and calculate the topological angles for such theories. Generically, these models will have fields with both linear and quadratic dispersion relations; for each $\mathcal{R}$, we determine how many fields of each dispersion type there are. Finally, for purely linearly-dispersing theories, we list the irreducible representations that also possess a $\mathbb{Z}_n$ symmetry that acts transitively on the $\text{SU}(n)/[\text{U}(1)]^{n-1}$ fields. Such SU($n$) chains have an 't Hooft anomaly in certain cases, allowing for a generalization of Haldane's conjecture to these novel representations. In particular, for even $n$ and for representations whose Young tableaux have two rows, of lengths $p_1$ and $p_2$ satisfying $p_1\not=p_2$, we predict a gapless ground state when $p_1+p_2$ is coprime with $n$. Otherwise, we predict a gapped ground state that necessarily has spontaneously broken symmetry if $p_1+p_2$ is not a multiple of $n$.

### Classical turning surfaces in solids: When do they occur, and what do they mean?

Classical turning surfaces of Kohn-Sham potentials, separating classically-allowed regions (CARs) from classically-forbidden regions (CFRs), provide a useful and rigorous approach to understanding many chemical properties of molecules. Here we calculate such surfaces for several paradigmatic solids. Our study of perfect crystals at equilibrium geometries suggests that CFRs are absent in metals, rare in covalent semiconductors, but common in ionic and molecular crystals. A CFR can appear at a monovacancy in a metal. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators. This classical picture is confirmed in the limits of extreme uniform compression of the internuclear distances, where all materials become metals without CFRs, and extreme expansion, where all materials become insulators with disconnected and widely-separated CARs around the atoms.

### Equilibrium mechanisms of self-limiting assembly

Self assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous self-organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states'': one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of {\it self-limiting assembly}, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits measure'' and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, examples of self-limiting assembly systems will be introduced and classified within this framework based on two broad categories: {\it self-closing assemblies} and {\it open-boundary assemblies}. These will include well-known cases -- micellization of amphiphiles and shell/tubule formation of tapered subunits -- as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

### Quantifying the interplay between fine structure and geometry of an individual molecule on a surface

The pathway toward the tailored synthesis of materials starts with precise characterization of the conformational properties and dynamics of individual molecules. Electron spin resonance based scanning tunneling microscopy can potentially address molecular structure with unprecedented resolution. Here, we determine the fine structure and geometry of an individual TiH molecule, utilizing a combination of a newly developed mK ESR-STM in a vector magnetic field and ab initio approaches. We demonstrate a strikingly large anisotropy of the g-tensor unusual for a spin doublet ground state, resulting from a non-trivial orbital angular momentum. We quantify the relationship between the resultant fine structure, hindered rotational modes, and orbital excitations. Our model system provides new avenues to determine the structure and dynamics of individual molecules with unprecedented precision.

### Topological Effects in Tunneling-Coupled Systems of One-Dimensional Quantum Rings

Using a model of idealized, crossed one-dimensional quantum wires we construct a novel model for a single electron on tunneling-coupled systems of one-dimensional quantum rings. We explore and find that topology can affect the energetics of the system, and can introduce frustration in the three ring case. We also study the special cases of an external magnetic field that controls the complex phase of the tunneling matrix element, and introduce the knot theory concept of "writhe" as a new topological quantity for distinguishing one hole systems. We find that writhe not only determines the energetic response of the system to magnetic field strength, but is also responsible for a single particle topological quantum phase transition involving the ground state wave function winding number.

### Reproducibility in high-throughput density functional theory: a comparison of AFLOW, Materials Project, and OQMD

A central challenge in high throughput density functional theory (HT-DFT) calculations is selecting a combination of input parameters and post-processing techniques that can be used across all materials classes, while also managing accuracy-cost tradeoffs. To investigate the effects of these parameter choices, we consolidate three large HT-DFT databases: Automatic-FLOW (AFLOW), the Materials Project (MP), and the Open Quantum Materials Database (OQMD), and compare reported properties across each pair of databases for materials calculated using the same initial crystal structure. We find that HT-DFT formation energies and volumes are generally more reproducible than band gaps and total magnetizations; for instance, a notable fraction of records disagree on whether a material is metallic (up to 7%) or magnetic (up to 15%). The variance between calculated properties is as high as 0.105 eV/atom (median relative absolute difference, or MRAD, of 6%) for formation energy, 0.65 {\AA}$^3$/atom (MRAD of 4%) for volume, 0.21 eV (MRAD of 9%) for band gap, and 0.15 $\mu_{\rm B}$/formula unit (MRAD of 8%) for total magnetization, comparable to the differences between DFT and experiment. We trace some of the larger discrepancies to choices involving pseudopotentials, the DFT+U formalism, and elemental reference states, and argue that further standardization of HT-DFT would be beneficial to reproducibility.

### Tunable lattice reconstruction and bandwidth of flat bands in magic-angle twisted bilayer graphene

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle {\theta}c. Experimentally, the {\theta}c is demonstrated to be very close to the magic angle ({\theta} ~ 1.05{\deg}). In this work, we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunnelling microscopy (STM). Our experiment demonstrates that both the two structures are stable in the TBG around the magic angle. By applying a STM tip pulse, we show that the two structures can be switched to each other and the bandwidth of the flat bands, which plays a vital role in the emergent strongly correlated states in the magic-angle TBG, can be tuned. The observed tunable lattice reconstruction and bandwidth of the flat bands provide an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.

### Ideal Unconventional Weyl Point in a Chiral Photonic Metamaterial

Unconventional Weyl points (WPs), carrying topological charge 2 or higher, possess interesting properties different from ordinary charge-1 WPs, including multiple Fermi arcs that stretch over a large portion of the Brillouin zone. Thus far, such WPs have been observed in chiral materials and acoustic metamaterials, but there has been no clean demonstration in photonics in which the unconventional photonic WPs are separated from trivial bands. We experimentally realize an ideal symmetry-protected photonic charge-2 WP in a three-dimensional topological chiral microwave metamaterial. We use field mapping to directly observe the projected bulk dispersion, as well as the two long surface arcs that form a noncontractible loop wrapping around the surface Brillouin zone. The surface states span a record-wide frequency window of around 22.7% relative bandwidth. We demonstrate that the surface states exhibit a novel topological self-collimation property and are robust against disorder. This work provides an ideal photonic platform for exploring fundamental physics and applications of unconventional WPs.

### Anomalous band renormalization due to high energy $kink$ in the colossal thermoelectric material K$_{0.65}$RhO$_2$

We report on low-energy electronic structure and electronic correlations of K$_{0.65}$RhO$_2$, studied using high-resolution angle-resolved photoemission spectroscopy (ARPES) technique and density functional theory (DFT) calculations. We observe a highly correlated hole pocket on the Fermi surface. We further notice that the correlations are momentum dependent. Most importantly, two $kinks$ at binding energies of 75 meV and 195 meV have been observed from the band dispersion in the vicinity of the Fermi level. While the low energy $kink$ at 75 meV can be understood as a result of the electron-phonon interaction, the presence of high energy $kink$ at 195 meV is totally a new discovery of this system leading to an anomalous band renormalization. Based on systematic analysis of our experimental data, we propose high frequency bosonic excitations as a plausible origin of the high energy anomaly. Further, we notice that the high energy anomaly has important implications in obtaining the colossal thermoelectric power of K$_{0.65}$RhO$_2$.

### Light-driven bandgap renormalization and terahertz atomic oscillations in few-layer PdSe2

Ultrashort light pulses allow real-time observation and direct control of non-equilibrium dynamics in low-dimensional systems to explore many-body physics that could be harnessed to design novel optoelectronic devices. As an emerging two-dimensional (2D) material, pentagonal palladium diselenide (PdSe2) possesses unconventionally high air stability, making it a promising candidate for next-generation optoelectronic devices. It is therefore desirable to understand its optical properties on ultrashort timescales and in a broadenergy range. Here we report on the use of 35 fs laser pulses to coherently drive and visualize the ultrafast dynamics of excited carriers, excitons, and phonons in few-layer PdSe2 based on broadband transient absorption spectroscopy spanning from the visible to the near-infrared. At high carrier densities, we observe a dramatic energy redshift of the main exciton transition of over 180 meV, indicating the presence of a giant bandgap renormalization which we attribute to strong screening provided by the photoexcited carriers. Additionally, we simultaneously visualize in real time two types of atomic oscillations, triggered by ultrashort light pulses, that couple preferentially to different types of electronic excitations: the intralayer (4.3 THz) coherent atomic motions to carriers and the interlayer (0.35 THz) motions to excitons. Combining Raman spectroscopy with first principles calculations, we identify the interplay between atomic vibrations and charge distribution as the microscopic mechanism driving these coherent interactions. Our findings provide direct insight and control into the many-body physics and non-equilibrium properties of free carriers, excitons, and phonons simultaneously, and therefore open new routes to concurrently manipulate electronic, optical, and vibrational properties of functional materials on the femtosecond timescale.

### Imaging the hybridized eigenmodes of a confined magnetic vortex resulting from propagating spiral spin waves from the core

The hybridized spin wave modes of a ferromagnetic vortex confined to a microscale disc have been directly observed in response to a microwave field excitation using time-resolved scanning Kerr microscopy. Micromagnetic simulations demonstrate that the observed curling nature of confined spin waves in the region of circulating in-plane magnetization is a result of the hybridization of different gyrotropic eigenmodes of the vortex core with the azimuthal (4 - 9 GHz) and radial (~10 GHz) eigenmodes of the in-plane magnetization. Hybridization with the fundamental gyrotropic mode leads to splitting of azimuthal modes with counter propagating wavevector, while hybridization of an azimuthal mode with the first-order gyrotropic mode allows the direction of the core gyration to be determined through hybridization rules. A higher frequency radial mode reveals evidence of excitation at the disc perimeter, but also evidence of hybridization with the first higher order gyrotropic mode. These experimental observations confirm the recent theoretical predictions of such hybridization. The measured spatio-temporal character of the hybridized modes is accurately reproduced by the simulations, which demonstrate that the mechanism for the hybridization is the emission of propagating short-wavelength spiral spin waves from the core. These results will have importance in the field of magnonics and spintronics that aim to utilize spin wave emission from highly localised, nanoscale regions of non-uniform magnetization, and their subsequent interaction with modes that may be supported nearby.

### Impurities in 3D quadratic band-touching Luttinger semimetals : Friedel and RKKY oscillations

We investigate the response of 3D Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an $1/r^4$ divergence of the responses, and anisotropic behavior. Certain of the spin-orbital signatures are robust to temperature, even if the charge and spin oscillations are smeared out, and give an unusual diamagnetic Pauli susceptibility. We compare our results to the experimental literature on the bismuth-based half-Heuslers such as YPtBi and on the pyrochlore iridate Pr$_2$Ir$_2$O$_7$.

### Composition heterogeneity influence on the phase formation dynamics in the Al-Y melt

It is shown that at a description of a binary solution, in the presence of a liquid phase of variable composition and a stoichiometric solid phase, the concept of chemical potential can be introduced for stoichiometry, which qualitatively describes the dynamics of the re-distribution of the impurity at the contact of the phases. A model describing the slow dynamics of diffusion processes in an initially inhomogeneous sample is proposed. In the model under study, it is shown that the interaction of the impurity and the phase composition of the mixture, when deviating from equilibrium, leads to the development of instability, known as spinodal decay and mathematically described by the Cahn-Hilliard equation. Within the framework of this model system, a dispersion relation is constructed, from which the growth rate of unstable fluctuations from time is found and the influence of the model parameters on the instability value is investigated. The detected instability can explain the processes of slow non-monotonic relaxation that occurs when melting glass-forming metal alloys.

### Dynamics of Holstein polaron in a chain with thermal fluctuations

Numerical modeling is used to investigate the dynamics of a polaron in a chain with small random Langevin-like perturbations which imitate the environmental temperature $T$ and under the influence of a constant electric field. In the semiclassical Holstein model the region of existence of polarons in the thermodynamic equilibrium state depends not only on temperature but also on the chain length. Therefore when we compute dynamics from initial polaron data, the mean displacement of the charge mass center differs for different-length chains at the same temperature. For a large radius polaron, it is shown numerically that the mean polaron displacement'' (which takes account only of the polaron peak and its position) behaves similarly for different-length chains during the time when the polaron persists. A similar slope of the polaron displacement enables one to find the polaron mean velocity and, by analogy with the charge mobility, assess the polaron mobility''. The calculated values of the polaron mobility for $T \approx 0$ are close to the value at $T=0$, which is small but not zero. For the parameters corresponding to the small radius polaron, simulations of dynamics demonstrate switching mode between immobile polaron and delocalized state. The position of the new polaron is not related to the position of the previous one; charge transfer occurs in the delocalized state.

### Charge-to-Spin Interconversion in Low-Symmetry Topological Materials

The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted not in a fundamental constraint but on the specific symmetries of traditionally studied systems. We theoretically show that the reduced symmetry of strong spin-orbit coupling materials such as ${\rm MoTe}_2$ or ${\rm WTe}_2$ enables new forms of intrinsic SHE that produce large and robust in-plane spin polarizations. Through quantum transport calculations on realistic device geometries with disorder, we show that the charge-to-spin interconversion efficiency can reach $\theta_{xy} \approx 80$\% and is gate tunable. The numerically extracted spin diffusion lengths ($\lambda_s$) are long and yield large values of the figure of merit $\lambda_s\theta_{xy}\sim 8\text{--}10$ nm, largely superior to conventional SHE materials. These findings vividly emphasize how crystal symmetry governs the intrinsic SHE, and how it can be exploited to broaden the range and efficiency of spintronic functionalities.

### Experimental evidence for topological phases in the magnetoconductance of 2DEG-based hybrid junctions

Several theoretical studies have recently predicted that the Majorana phases could be realized as quantized plateaus in the magnetoconductance of the artificially engineered hybrid junctions based on two-dimensional electron gases (2DEG) under fully out-of-plane magnetic fields. The large transverse Rashba spin-orbit interaction in 2DEG together with a strong orbital effect due to magnetic fields yield topological phase transitions to nontrivial phases hosting Majorana modes. Such Majorana modes are formed at the ends of 2DEG-based wires with a hybrid superconductor-semiconductor integrity. Here, we report on the experimental observation of such topological phases in hybrid junctions on an In0.75Ga0.25As 2DEG platform by sweeping small out-of-plane magnetic fields (B< 100 mT) and probing the conductance to highlight the characteristic quantized magnetoconductance plateaus. The observed signature of topological phases in small out-of-plane magnetic fields in planar hybrid junctions suggests that In0.75Ga0.25As heterostructure affords a promising material platform for the realization of scalable topological circuits for the applications in quantum technologies.

### Waveguide quantum optomechanics: parity-time phase transitions in ultrastrong coupling regime

We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest set-up of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (\PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The $\mathcal{PT}$ phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.

### Origin of enhanced chemical precompression in cerium hydride CeH$_{9}$

The rare-earth metal hydrides with clathrate structures have been highly attractive because of their promising high-$T_{\rm c}$ superconductivity at high pressure. Recently, cerium hydride CeH$_9$ composed of Ce-encapsulated clathrate H cages was synthesized at much lower pressures of 80$-$100 GPa, compared to other experimentally synthesized rare-earth hydrides such as LaH$_{10}$ and YH$_6$. Based on density-functional theory calculations, we find that the Ce 5$p$ semicore and 4$f$/5$d$ valence states strongly hybridize with the H 1$s$ state, while a transfer of electrons occurs from Ce to H atoms. Further, we reveal that the delocalized nature of Ce 4$f$ electrons plays an important role in the chemical precompression of clathrate H cages. Our findings not only suggest that the bonding nature between the Ce atoms and H cages is characterized as a mixture of ionic and covalent, but also have important implications for understanding the origin of enhanced chemical precompression that results in the lower pressures required for the synthesis of CeH$_9$.

### Data-Mining Element Charges in Inorganic Materials

Oxidation states are well-established in chemical science teaching and research. We data-mine more than 168,000 crystallographic reports to find an optimal allocation of oxidation states to each element. In doing so we uncover discrepancies between text-book chemistry and reported charge states observed in materials. We go on to show how the oxidation states we recommend can significantly facilitate materials discovery and heuristic design of novel inorganic compounds.

### Tensor monopoles and negative magnetoresistance effect in four-dimensional optical lattices

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to quantum metric tensor in even dimensions, can be simulated by ultracold atoms in the optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find a negative relative magnetoresistance effect of approximately $-B^{2}$ dependence when a hyperplane is cut through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by extending an artificial dimension in 3D optical lattices. Moreover, we show that the quantum metric tensor can be detected by applying an external drive in the optical lattices.

### On the Variability of Critical Size for Homogeneous Nucleation in a Solid-State Diffusional Transformation

In a solid-state diffusional phase transformation involving nucleation and growth, the size of the critical nucleus for a homogeneous process (r*homo=r* ) has been assumed to be a time invariant constant of the transformation. The strain associated with the process has a positive energy contribution and leads to an increase in the value of r*, with respect to that for nucleation from a liquid. With the progress of such a transformation, the strain energy stored in the matrix increases and nuclei forming at a later stage encounter a strained matrix. Using devitrification of a bulk metallic glass as a model system, we demonstrate that r* is not a cardinal time invariant constant for homogeneous nucleation and can increase or decrease depending on the strain energy penalty. We show that the assumption regarding the constancy of r* is true only in the early stages of the transformation and establish that the progress of the transformation leads to an altered magnitude of r*, which is a function of the microstructural details, geometrical variables and physical parameters. With the aid of high-resolution lattice fringe imaging and computations of r*, we further argue that, 'liquid-like' homogeneous nucleation can occur and that the conclusions are applicable to a broad set of solid-state diffusional transformations. The above effect 'opens up' a lower barrier transformation pathway arising purely from the internal variables of the system.

### Soft matter science and the COVID-19 pandemic

Much of the science underpinning the global response to the COVID-19 pandemic lies in the soft matter domain. Coronaviruses are composite particles with a core of nucleic acids complexed to proteins surrounded by a protein-studded lipid bilayer shell. A dominant route for transmission is via air-borne aerosols and droplets. Viral interaction with polymeric body fluids, particularly mucus, and cell membranes control their infectivity, while their interaction with skin and artificial surfaces underpins cleaning and disinfection and the efficacy of masks and other personal protective equipment. The global response to COVID-19 has highlighted gaps in the soft matter knowledge base. We survey these gaps and suggest questions that can (and need to) be tackled, both in response to COVID-19 and to better prepare for future viral pandemics.

### Chemical and hydrostatic pressure tuning of the ground state in ZrFe$_4$Si$_2$

In ZrFe$_4$Si$_2$ we studied the ground-state properties and their evolution with chemical substitution of Ge on the Si site and under hydrostatic pressure using structural, magnetic, thermodynamic, and electrical-transport probes. Magnetic measurements reveal that ZrFe$_4$Si$_2$ holds paramagnetic Fe moments with an effective moment $\mu_{\rm eff}= 2.18~\mu_{B}$. At low temperatures the compound have a weak short-range magnetic order below 6 K. Our studies demonstrate that substituting Ge for Si increases the unit-cell volume and stabilizes the short-range order into a long-range spin-density wave type magnetic order. On the other hand, hydrostatic pressure studies using electrical-resistivity measurements on ZrFe$_4$(Si$_{0.88}$Ge$_{0.12}$)$_2$ indicate a continuous suppression of the magnetic ordering upon increasing pressure. Our combined chemical substitution and hydrostatic pressure studies therefore suggest the existence of a lattice-volume controlled quantum critical point in ZrFe$_4$Si$_2$.

### Electronic Properties of Graphene Quantum Ring with Wedge Disclination

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel functions and their asymptotic behavior allows to derive quantized energy levels in the presence of an energy gap. We also investigate the persistent currents that appear in the quantum ring and how wedge disclination influences different quantum transport quantities.

### Entropy-reduced retention times in magnetic memory elements: A case of the Meyer-Neldel Compensation Rule

We compute mean waiting times between thermally-activated magnetization reversals in a nanodisk with parameters similar to a free CoFeB layer used in magnetic random access memories. By combining Langer's theory and forward flux sampling simulations, we show that the Arrhenius prefactor can take values up to 10$^{21}$ Hz, orders of magnitude beyond the value of 10$^{9}$ Hz typically assumed, and varies drastically as a function of material parameters. We show that the prefactor behaves like an exponential of the activation energy, which highlights a case of the Meyer-Neldel compensation rule. This suggests that modeling information retention times with a barrier-independent prefactor in such magnetic storage elements is not justified.

### Induced interactions and quench dynamics of bosonic impurities immersed in a Fermi sea

We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. Following a quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase-separation between the impurities and their surrounding for strong repulsions. For attractive post-quench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between non-interacting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

### Distribution of Topological Types in Grain-Growth Microstructures

An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these distributions in two- and three-dimensional systems. In particular, a bending-like energy $E_i$ is associated to each grain topology $t_i$, and the probability of observing that particular topology is proportional to $\frac{1}{s(t_i)}e^{-\beta E_i}$, where $s(t_i)$ is the order of an associated symmetry group and $\beta$ is a thermodynamic-like constant. We explain the physical origins of this approach, and provide numerical evidence in support.

### Synthesis of FeNi tetrataenite phase by means of chemical precipitation

FeNi L10 (tetrataenite) phase has great perspectives for hard magnetic materials production. In this paper it was synthesized in chemically co-precipitated FeNi nanopowder by means of thermal treating included cycling of oxidation and reduction processes at 320 {\deg}C. The presence of FeNi L10 phase in the samples was confirmed by magnetic measurements and DSC analysis.

### Classification of the symmetry of photoelectron dichroism broken by light

We investigate how the direction of polarized light can affect the dichroism pattern seen in angle-resolved photoemission spectroscopy. To this end, we prepared a sample composed of highly-oriented Bi(111) micro-crystals that macroscopically has infinite rotational and mirror symmetry of the point group $\rm{C}_{\infty\rm{v}}$ and examined whether the dichroism pattern retains the $\rm{C}_{\infty\rm{v}}$ symmetry under the stationary configuration of the light and sample. The direction of the light was imprinted in the pattern. Thereby, we apply group theory and classify the pattern with the configuration of light taken into account. We complete the classification by discussing the cases when the out-of-plane component of the polarization can be neglected, when the incidence angle is either 0$^{\circ}$ or 90$^{\circ}$, when the polarization is either elliptic or linear, and also when the sample is a crystal.

### Micromagnetic modelling of nanorods array-based L10-FeNi/SmCo5 exchange-coupled composites

Exchange-coupled nanocomposites are considered as the most promising materials for production of high-energy performance permanent magnets, which can exceed neodymium ones in terms of energy product. In this work, micromagnetic simulations of L10-FeNi/SmCo5 composites based on the initially anisotropic structure of nanorods array were performed. Texturing effect on magnetic properties was investigated. It was revealed that even 30 % of anisotropy axes misalignment of grains in L10-FeNi phase would lead to only 10 % drop of coercivity. To maximize magnetic properties of the composites, parameters of microstructure were optimized for 120 x 120 array of interacting nanorods and were found to be 40 nm nanorod diameter and 12-20 nm interrod distance. The estimated diameter of nanorods and the packing density of the array provide energy product values of 149 kJ m-3. Influence of interrod distance on energy product values was explored. Approaches for production of exchange-coupled composites based on anisotropic nanostructures were proposed.

### Design of nematic liquid crystals to control microscale dynamics

Dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in areas such as the transformation of stored or environmental energy into systematic motion, micro-robotics, and transport of matter at the microscale. This overview presents an approach to command microscale dynamics by replacing an isotropic medium such as water with an anisotropic fluid, a nematic liquid crystal. Orientational order leads to new dynamic effects, such as propagation of particle-like solitary waves. Many of these effects are still awaiting their detailed mathematical description. By using plasmonic metamask photoalignment, the nematic director can be patterned into predesigned structures that control dynamics of inanimate particles through the liquid crystal enabled nonlinear electrokinetics. Moreover, plasmonic patterning of liquid crystals allows one to command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and concentration in space. The patterned director design can also be extended to liquid crystal elastomers, in which case the director gradients define the dynamic profile of elastomer coatings. Some of these systems form an experimental playground for the exploration of out-of-equilibrium active matter, in which the levels of activity, degree of orientational order and patterns of alignment can all be controlled independently of each other.

### Kondo physics in antiferromagnetic Weyl semimetal Mn3+xSn1-x films

Topology and strong electron correlations are crucial ingredients in emerging quantum materials, yet their intersection in experimental systems has been relatively limited to date. Strongly correlated Weyl semimetals, particularly when magnetism is incorporated, offer a unique and fertile platform to explore emergent phenomena in novel topological matter and topological spintronics. The antiferromagnetic Weyl semimetal Mn3Sn exhibits many exotic physical properties such as a large spontaneous Hall effect and has recently attracted intense interest. In this work, we report synthesis of epitaxial Mn3+xSn1-x films with greatly extended compositional range in comparison with that of bulk samples. As Sn atoms are replaced by magnetic Mn atoms, the Kondo effect, which is a celebrated example of strong correlations, emerges, develops coherence, and induces a hybridization energy gap. The magnetic doping and gap opening lead to rich extraordinary properties as exemplified by the prominent DC Hall effects and resonance-enhanced terahertz Faraday rotation.

### Size and temperature dependent magnetization of iron nanoclusters

The magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated via spin dynamics (SD) simulations coupled to molecular dynamics (MD), using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, reaching the Curie temperature. Comparisons with experimental data and theoretical models based on the mean-field Ising model are also presented, including one adapted to small clusters, and another developed to take into account the influence of low coordinated spins at free surfaces. Magnetization results show excellent agreement with experimental measurements for small Fe nanoclusters. Large differences are found with frozen-atom simulations. Finite-size effects on the thermal behavior of the magnetization increase as the size of the clusters is reduced, especially near the Curie temperature, Tc. Analytical approximations to the magnetization as a function of temperature and size are proposed.

### Imaging the topological current carrying state and the surface to bulk transformation, in Bi2Se3 single crystal and thin film

Magneto-optics based current imaging technique compares the nature of topological current distribution in a single crystal and thin film of topological insulator material, Bi2Se3. The single crystal, at low temperatures, has uniform topological surface current sheets which are about 3.6 nm thick. With increasing temperature, the current partially diverts into the crystal bulk and concomitantly, the sheet break up into a patchy network of high and low current density regions. The temperature dependence of the high current density areas shows that the surface to bulk transformation in the crystal has features of classical phase transition phenomena. The surface area fraction with topological high current density behaves like an order parameter. This phase transition is driven by disorder. In Bi2Se3 thin film we show the presence of quasi one-dimensional topological edge currents which are suppressed with a weak applied magnetic field. The edge current transforms into a uniform bulk current in the film.

### Topological transition from superuid vortex rings to isolated knots and links

Knots and links are fundamental topological objects play a key role in both classical and quantum fluids. In this research, we propose a novel scheme to generate torus vortex knots and links through the reconnections of vortex rings perturbed by Kelvin waves in trapped Bose-Einstein condensates. We observe a new phenomenon in a confined superfluid system in which the transfer of helicity between knots/links and coils can occur in both directions with different pathways. The pathways of topology transition can be controlled through designing specific initial states. The generation of a knot or link can be achieved by setting the parity of the Kelvin wave number. The stability of knots/links can be improved greatly with tunable parameters, including the ideal relative angle and the minimal distance between the initial vortex rings.

### Ultrahigh efficient spin-orbit torque magnetization switching in all-sputtered topological insulator - ferromagnet multilayers

Spin-orbit torque (SOT) magnetization switching of ferromagnets with large perpendicular magnetic anisotropy has a great potential for the next-generation non-volatile magnetoresistive random-access memory (MRAM). It requires a high-performance pure spin current source with a large spin Hall angle and high electrical conductivity, which can be fabricated by a mass production technique. In this work, we demonstrate ultrahigh efficient and robust SOT magnetization switching in all-sputtered BiSb topological insulator - perpendicularly magnetized Co/Pt multilayers. Despite fabricated by the industry-friendly magnetron sputtering instead of the laboratory molecular beam epitaxy, the topological insulator layer, BiSb, shows a large spin Hall angle of $\theta$$_{SH}$ = 12.3 and high electrical conductivity of $\sigma$ = 1.5x$10^5$ $\Omega^{-1}$m$^{-1}$. Our results demonstrate the mass production capability of BiSb topological insulator for implementation of ultralow power SOT-MRAM and other SOT-based spintronic devices.

### Turbulent cascade induced persistent current of cold atomic superfluids

Dissipating of disorder quantum vortices in an annular two-dimensional Bose-Einstein condensate can form a macroscopic persistent flow of atoms. We propose a protocol to create persistent flow with high winding number based on a double concentric ring-shaped configuration. We find that a sudden geometric quench of the trap from single ring-shape into double concentric ring-shape will enhance the circulation flow in the outer ring-shaped region of the trap when the initial state of the condensate is with randomly distributed vortices of the same charge. The circulation flows that we created are with high stability and good uniformity free from topological excitations. Our study is promising for new atomtronic designing, and is also helpful for quantitatively understanding quantum tunneling and interacting quantum systems driven far from equilibrium.

### Coherence of an extended central spin model with a coupled spin bath

We study an extended central spin model with an isotropic nearest-neighbour spin-exchange interaction among the bath spins. The system is controllable by external magnetic fields applied on the central spin and the bath, respectively. We construct a basis set of the Hilbert space and express the Hamiltonian of the extended model into a series of $2\times2$ block matrices to obtain the exact solution of the model successfully. Therefrom, the coherence and the spin polarization of the central spin are investigated. We find that if the couplings among the bath spins are antiferromagnetic, the central spin has good coherence and polarization at low temperatures. Moreover, the decoherence is greatly suppressed at the critical point where the strengthes of the central and the bath magnetic field take the same value. A dephasing phenomenon is identified when the initial state of the central spin is unpolarized.

### Electron Transmission Across Normal Metal-Strained Graphene-Normal Metal Junctions

The transmission of the electron across the single normal metal-graphene (NG) and normal-metal-graphene-normal-metal (NGN) junctions has been investigated. For the single NG junction, the profile of the maximum transmission which has been plotted against the dimensionless interface hopping respectively bears similarity to that of the conductance of the system. The minor effect of the incidence energy on transmission can also be found in conductance of the single NG junction whose tunneling behavior poses a striking difference from that of the NGN junction. Concerning with NGN junction, the transmission and conductance show more abundant structures when subjected to different incidence energies, interface hopping, and strain strengths. The increase of strain strength always induces more resonance peaks at different angles in transmission and can therefore enhance the conductance. The increase of length of the middle graphene segment can accommodate more quasi-resonance states, leading to the more resonance peaks and richer structures in transmission. In both single NG and NGN junctions, the increase of the wavefunction period on metal side(s) can be observed due to the enhancement of strain strength, which can serve as the sensor for the detection of the strain strength in graphene.

### Systemic Performance Measures from Distributional Zeta-Function

We propose the use of the Distributional Zeta-Function (DZF) for constructing a new set of Systemic Performance Measures (SPM). SPM have been proposed to investigate network synthesis problems such as the growing of linear consensus networks. The adoption of the DZF has shown interesting physical consequences that in the usual replica method are still unclarified, i.e., the connection between the spontaneous symmetry breaking mechanism and the structure of the replica space in the disordered model. We relate topology of the network and the partition function present in the DZF by using the spectral and the Hamiltonian structure of the system. The studied objects are the generalized partition funcion, the DZF, the Expected value of the replica partition function, and the quenched free energy of a field network. We show that with these objects we need few operations to increase the percentage of performance enhancement of a network. Furthermore, we evalue the location of the optimal added links for each new SPM and calculate the performance improvement of the new network for each new SPM via the spectral zeta function, $\mathcal{H}_{2}$-norm, and the communicability between nodes. We present the advantages of this new set of SPM in the network synthesis and we propose other methods for using the DZF to explore some issues such as disorder, critical phenomena, finite-temperature, and finite-size effects on networks. Relevance of the results are discussed.

### Viscosity of two-dimensional electrons

The hydrodynamic regime of electron transport has been recently realized in conductors with ultra-low densities of defects. Although many theoretical works have been devoted to studies of relaxation processes in two-dimensional (2D) electron fluids, the viscosity of the realistic Fermi gas of 2D electrons interacting by Coulomb's law has not been reliably determined up to now either in theory or in experiment. Here we construct a theory of viscosity and thermal conductivity in such system. We compare the previously known viscosity of a 2D Fermi liquid and our result for the viscosity of a 2D electron Fermi gas with available experimental data extracted from the hydrodynamic negative magnetoresistance observed on the best-quality GaAs quantum wells. Based on a good agreement between theory and experiment, we conclude that measurements of the temperature dependence of the viscosity is a direct method (i) to identify the hydrodynamic regime of electron transport and (ii) to trace the transition between an electron Fermi liquid and a Fermi gas.

### Stress-strain in electron-beam activated polymeric micro-actuators

Actuation of thin polymeric films via electron irradiation is a promising avenue to realize devices based on strain engineered two dimensional (2D) materials. Complex strain profiles demand a deep understanding of the mechanics of the polymeric layer under electron irradiation; in this article we report a detailed investigation on electron-induced stress on poly-methyl-methacrylate (PMMA) thin film material. After an assessment of stress values using a method based on dielectric cantilevers, we directly investigate the lateral shrinkage of PMMA patterns on epitaxial graphene, which reveals a universal behavior, independent of the electron acceleration energy. By knowing the stress-strain curve, we finally estimate an effective Young's modulus of PMMA on top of graphene which is a relevant parameter for PMMA based electron-beam lithography and strain engineering applications.

### Clarifying multiple-tip effects on Scanning Tunneling Microscopy imaging of 2D periodic objects and crystallographic averaging in the spatial frequency domain

Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from a sample that is periodic in two dimensions. The image-forming current for multiple tips in STM is derived in a more straightforward manner than prior approaches. The Fourier spectrum of the current for p4mm Bloch surface wave functions and a pair of delta function tips reveals the tip-separation dependence of various types of image obscurations. In particular our analyses predict that quantum interference should be visible on a macroscopic scale in the form of bands quite distinct from the basket-weave patterns a purely classical model would create at the same periodic double STM tip separations. A surface wave function that models the essential character of highly (0001) oriented pyrolytic graphite (technically known as HOPG) is introduced and used for a similar tip-separation analysis. Using a bonding H_2 tip wave function with significant spatial extent instead of this pair of infinitesimal Dirac delta function tips does not affect these outcomes in any observable way. This is explained by Pierre Curie's well known symmetry principle. Classical simulations of multiple tip effects in STM images may be understood as modeling multiple tip effects in images that were recorded with other types of SPMs). Our analysis clarifies why CIP and crystallographic averaging work well in removing the effects of a blunt SPM tip (that consist of multiple mini-tips) from the recorded 2D periodic images and also outlines the limitations of this image processing techniques for certain spatial separations of STM mini-tips.

### Graphane -- material for hydrogen storage, breathers and kinks

In this paper we study the graphane. The Frenkel-Kontorova model on hexagonal lattice was used. We studied the case of one H atom above the C atom in the plane of graphane (we used the approximation of the hexagonal lattice in the plane). Continuous limit of the Lagrange-Euler equations is found from the Hamiltonian for $H$ atoms motion, they enabled us to study kink and breather excitations of $H$ atoms in the $H$ plane above the $C$ plane. We have found that there are three cases in the one $H$ atom motion The case $1$, when the $H$ atom is at the position which is below the position at which it is desorbed. Then the motion of this $H$ atom at time $t_{h}$ is described. The case $2$, when the $H$ atom is at the position of the suppressed atom $H$ in the direction to the $C$ (nearer) atom. This $H$ atom will be desorbed from the graphane going through the minimum of the potential energy and then through the point of desorption. Its motion of at time $t_{h}$ is described. The case $3$, when the $H$ atom is near the position of small oscillations near the potential energy minimum. The position of the atom $H$ at the time $t_{0}$ is the position to which the atom $H$ was excited with external force. The lattice of $H$ atoms in graphane may be excited as described by the kink solution of the Sine-Gordon equation. The kink has its velocity $U$, $U^{2} < 1$, and in time $T$ and in $X^{'}$ coordinate direction localization. The Sine-Gordon equation has the breather solution in the $X^{'}$ direction. There $\omega$ is the frequency of the breather, $T_{0}$ and $X^{'}_{0}$ are in time $T$ and in $X^{'}$ direction localization.

### Singular mean-field states: A brief review of recent results

This article provides a focused review of recent findings which demonstrate, in some cases quite counter-intuitively, the existence of bound states with a singularity of the density pattern at the center, while the states are physically meaningful because their total norm converges. One model of this type is based on the 2D Gross-Pitaevskii equation (GPE) which combines the attractive potential ~ 1/r^2 and the quartic self-repulsive nonlinearity, induced by the Lee-Huang-Yang effect (quantum fluctuations around the mean-field state). The GPE demonstrates suppression of the 2D quantum collapse, driven by the attractive potential, and emergence of a stable ground state (GS), whose density features an integrable singularity ~1/r^{4/3} at r --> 0. Modes with embedded angular momentum exist too, and they have their stability regions. A counter-intuitive peculiarity of the model is that the GS exists even if the sign of the potential is reversed from attraction to repulsion, provided that its strength is small enough. This peculiarity finds a relevant explanation. The other model outlined in the review includes 1D, 2D, and 3D GPEs, with the septimal (seventh-order), quintic, and cubic self-repulsive terms, respectively. These equations give rise to stable singular solitons, which represent the GS for each dimension D, with the density singularity ~1/r^{2/(4-D). Such states may be considered as a result of screening of a "bare" delta-functional attractive potential by the respective nonlinearity.

### Effect of microstructure on polymer chain dynamics in polyethylene glycol solutions

Effect of microstructures and interactions on segmental dynamics in polyethylene glycol (PEG) solution in water is probed with macro-scale oscillatory rheology and micro-scale diffusion of a fluorescent probe. PEG solution fluorescence recovery after photobleaching (FRAP) curves have immobile fractions which increase with PEG concentration, for PEG volume fraction (c) > 0.2, indicating structuring. PEG solution micro-scale diffusion coefficients follow Rouse scaling D {\ alpha} c^(-0.54) for c < 0.8, resembling unentangled neutral polymers in good solvent. Addition of nanoclay bentonite (B) in PEG matrix slows down probe diffusion 3-7 times, with heterogeneous dynamics. With addition of carboxymethyl cellulose (CMC) in PEG matrix, probe diffusion is homogeneous with negligibly small enhancement in diffusion time. The macroscale storage modulii for PEG, PEG+B, and PEG + CMC solutions scale as viscous fluid-like, followed by short elastic plateau. Beyond the elastic plateau, the scaling is a concentration-dependent power law greater than the Rouse scaling of 0.5 for 0.1{\tau}_b^(-1) , Rouse scaling is recovered. Addition of CMC to PEG also restores Rouse scaling. Addition of B gives contributions from both polymer matrix and network of B particles, leading to departure from pure Rouse behaviour. Static microstructural studies reveal clay aggregation due to depletion interactions on increasing the concentration of clay particles in PEG matrix, which leads to a non-monotonic concentration dependence of storage modulus with c.

### Large deviations of the ballistic Lévy walk model

We study the ballistic L\'evy walk and obtain the far-tail of the distribution for the walker's position. When the position is of the order of the observation time, its distribution is described by the well-known Lamperti-arcsine law. However this law blows up at the far-tail which is nonphysical, in the sense that any finite time observation will never diverge. We claim that one can find two laws for the position of the particle, the first one is the mentioned Lamperti-arcsine law describing the central part of the distribution and the second is an infinite density illustrating the far tail of the position. We identify the relationship between the largest position and the longest waiting time describing the single big jump principle.From the renewal theory we find that the distribution of rare events of the position is related to the derivative of the average of the number of renewals at a small time' using a rate formalism.

### Electrically switchable Rashba-type Dzyaloshinskii-Moriya interaction and skyrmion in two-dimensional magnetoelectric multiferroics

Realizing topological magnetism and its electric control are intensive topics in the spintronics due to their promising applications in information storage and logic technologies. Here we unveil that both can be achieved in the two-dimensional (2D) magnetoelectric multiferroics. Using first-principles calculations, we show that strong Dzyaloshinskii-Moriya interaction (DMI), which is the key ingredient for the formation of exotic chiral magnetism, could be induced in 2D multiferroics with vertical electric polarization via Rashba effect. We verify that such significant DMI can promote sub-10 nm skyrmion in 2D multiferroics with perpendicular magnetic anisotropy such as CrN monolayer. In addition, the presence of both magnetization and electric polarization in 2D multiferroics provides us unique opportunity for the effective electric control of both strength and chirality of DMI and thereby the topological magnetism. As an example, we introduce the four multiferroic skyrmions with different chirality and polarity that can be manipulated by external field.

### Criteria for room temperature topological transport

It is often quoted that novel electronic devices based on topological states can operate at room temperature, but empirically it is not clear if this is truly possible. Here we develop simple criteria for the maximum temperature at which the topological surface states or edge states could dominate the electrical transport properties, a necessity for a topological device. This is demonstrated for 3-dimensional topological insulators (TIs) and 1D quantum anomalous Hall insulators (QAHIs), though this can be applied to similar systems. The density of thermally activated carriers gives the upper temperature when topological surfaces may dominate transport. By considering the space of band gap, dielectric constant, and effective mass, a clear boundary emerges that separates current TIs materials from those that may operator at or above room temperature, and, thus, providing clear criteria to search for next-generation materials. For QAHIs, current materials are also far from the room temperature limit, but liquid nitrogen temperatures may be within reach, especially considering heterostructures with magnetic materials. Establishing these specific criteria is crucial to design new materials systems, which is key to pushing into a new generation of topological technologies.

### Spectral rigidity of non-Hermitian symmetric random matrices

We study the spectral rigidity of the non-Hermitian analog of the Anderson model suggested by Tzortzakakis, Makris and Economou (TME). This is a $L\times L \times L$ tightly bound cubic lattice, where both real and imaginary parts of on-site energies are independent random variables uniformly distributed between $-W/2$ and $W/2$. The TME model may be used to describe a random laser. In a recent paper we proved that this model has the Anderson transition at $W= W_c \simeq 6$ in three-dimensional case. Here we numerically diagonalize TME $L \times L \times L$ cubic lattice matrices and calculate the number variance of eigenvalues in a disk of the complex plane. We show that on the metallic side $W < 6$ of the Anderson transition, complex eigenvalues repel each other as strongly as in the complex Ginibre ensemble only in a disk containing $N_c(L,W)$ eigenvalues. Similarly to the number of energy levels $N_c$ in the energy band with the Thouless energy $E_c$ width in the Anderson model, we find that in TME model $N_c(L,W)$ is proportional to $L$ and grows with decreasing $W$.

### Configurational Mean-Field Reduced Transfer Matrix Method for Ising Systems

A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff's mean-field approach with the model presented by one of us previously. The mean-field approximation is introduced with the replacement of the central spin in Ising Hamiltonian with an average value of particular spin configuration, i.e, the approximation is taken into account within each configuration. This approximation is used in two different mean-field-type approaches. The first consideration is a pure-mean-field-type treatment in which all the neighboring spins are replaced with the assumed configurational average. The second consideration is introduced by the reduced transfer matrix method. The estimations of critical coupling values of the systems are evaluated both numerically and also analytically by the using of saddle point approximation. The analytical estimation of critical values in the first and second considerations are $K_{c}=\frac{1}{z}$ and $(z-2) K_{c}e^{2K_{c}} =1$ respectively. Obviously, both of the considerations have some significant deviation from the exact treatment. In this work, we conclude that the method introduced here is more appropriate physical picture than self-consistent mean-field-type models, because the method introduced here does not presume the presence of the phase transition from the outset. Consequently, the introduced approach potentially makes our research very valuable mean-field-type picture for phase transition treatment.

### Formation dynamics of black- and white-hole horizons in an analogue gravity model

We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks-Girardeau gas) we show that, by switching on a step potential, either a sonic (black-hole-like) horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated white-hole horizon, although a stable stationary solution of the dynamical equations with those properties is analytically found. Moreover, we show that the semiclassical dynamics, based on the Gross-Pitaevskii equation, conforms to the exact solution only in the case of fully subsonic flows while a stationary solution exhibiting a supersonic transition is never reached dynamically.

### Novel magnetic states and nematic spin chirality in the kagome lattice metal YMn$_{6}$Sn$_{6}$

Identification, understanding, and manipulation of novel magnetic textures is essential for the discovery of new quantum materials for future spin-based electronic devices. In particular, materials that manifest a large response to external stimuli such as a magnetic field are subject to intense investigation. Here, we study the kagome-net magnet YMn$_{6}$Sn$_{6}$ by magnetometry, transport, and neutron diffraction measurements combined with first principles calculations. We identify a number of nontrivial magnetic phases, explain their microscopic nature, and demonstrate that one of them hosts a large topological Hall effect (THE). We propose a new nematic chirality mechanism, reminiscent of the nematicity in Fe-based superconductors, which leads to the THE at elevated temperatures. This interesting physics comes from parametrically frustrated interplanar exchange interactions that trigger strong magnetic fluctuations. Our results pave a path to new chiral spin textures, promising for novel spintronics.

### Topological versus spectral properties of random geometric graphs

In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space. RGGs, $G(n,\ell)$, consist of $n$ vertices uniformly and independently distributed on the unit square, where two vertices are connected by an edge if their Euclidian distance is less or equal than the connection radius $\ell \in [0,\sqrt{2}]$. To evaluate the topological properties of RGGs we chose two well-known topological indices, the Randi\'c index $R(G)$ and the harmonic index $H(G)$. While we characterize the spectral and eigenvector properties of the corresponding randomly-weighted adjacency matrices by the use of random matrix theory measures: the ratio between consecutive eigenvalue spacings, the inverse participation ratios and the information or Shannon entropies $S(G)$. First, we review the scaling properties of the averaged measures, topological and spectral, on RGGs. Then we show that: (i) the averaged--scaled indices, $\left\langle R(G) \right\rangle$ and $\left\langle H(G) \right\rangle$, are highly correlated with the average number of non-isolated vertices $\left\langle V_\times(G) \right\rangle$; and (ii) surprisingly, the averaged--scaled Shannon entropy $\left\langle S(G) \right\rangle$ is also highly correlated with $\left\langle V_\times(G) \right\rangle$. Therefore, we suggest that very reliable predictions of eigenvector properties of RGGs could be made by computing topological indices.

### Spectroscopic Evidence for Charge Order Melting via Quantum Fluctuations in a Cuprate

Copper-oxide high TC superconductors possess a number of exotic orders co-existing with or proximal to superconductivity, whose quantum fluctuations may account for the unusual behaviors of the normal state, even affecting superconductivity. Yet, spectroscopic evidence about such quantum fluctuations remains elusive. Here, we reveal spectroscopic fingerprints for such fluctuations associated with a charge order (CO) in nearly optimally-doped Bi2Sr2CaCu2O8+d, using resonant inelastic x-ray scattering (RIXS). In the superconducting state, while the quasi-elastic CO signal decreases with temperature, the interplay between CO fluctuations and bond-stretching phonons in the form of a Fano-like interference paradoxically increases, incompatible with expectations for competing orders. Invoking general principles, we argue that this behavior reflects the properties of a dissipative system near an order-disorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations which melt CO.

### Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models

Non-Hermitian generalizations of the Su-Schrieffer-Heeger (SSH) models with higher periods of the hopping coefficients, called the SSH3 and SSH4 models, are analyzed. Although the one-dimensional Hermitian SSH3 model is topologically trivial, the non-Hermitian generalization leads to a topological system due to a point gap on the complex plane. The non-Hermitian SSH3 model is characterized by the winding number and exhibits the non-Hermitian skin effect. Moreover, the SSH3 model has localized states and zero-energy state not associated with the topology. Meanwhile, the SSH4 model resembles the SSH model, and its non-Hermitian generalization also exhibits the non-Hermitian skin effect. A careful analysis of the non-Hermitian SSH4 model with different boundary conditions shows the bulk-boundary correspondence is restored with the help of the generalized Brillouin zone or the real-space winding number. The physics of the non-Hermitian SSH3 and SSH4 models may be tested in cold-atom or other simulators.

### Observation of phonon trapping in the continuum with topological charges

Phonon trapping has an immense impact in many areas of science and technology, from the antennas of interferometric gravitational wave detectors to chip-scale quantum micro- and nano-mechanical oscillators. It usually relies on the mechanical suspension--an approach, while isolating selected vibrational modes, leads to serious drawbacks for interrogation of the trapped phonons, including limited heat capacity and excess noises via measurements. To circumvent these constraints, we realize a new paradigm of phonon trapping using mechanical bound states in the continuum (BICs) with topological features and conducted an in-depth characterization of the mechanical losses both at room and cryogenic temperatures. Our findings of mechanical BICs combining the microwave frequency and macroscopic size unveil a unique platform for realizing mechanical oscillators in both classical and quantum regimes. The paradigm of mechanical BICs might lead to unprecedented sensing modalities for applications such as rare-event searches and the exploration of the foundations of quantum mechanics in unreached parameter spaces.

### Detection of quantum geometric tensor by nonlinear optical response

Quantum geometric tensor (QGT), including a symmetric real part defined as quantum metric and an antisymmetric part defined as Berry curvature, is essential for understanding many phenomena. We studied the photogalvanic effect of a multiple-band system with time-reversal-invariant symmetry by theoretical analysis in this work. We concluded that the integral of gradient of the symmetric part of QGT in momentum space is related to the linearly photogalvanic effect, while the integral of gradient of Berry curvature is related to the circularly photogalvanic effect. Our work afforded an alternative interpretation for the photogalvanic effect in the view of QGT, and a simple approach to detect the QGT by nonlinear optical response.

### Exact solutions of directed walk models of polymeric zipping with pulling in two and three dimensions

We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the solutions are written in terms of complete elliptic integrals. We analyse the phase transition associated with each model giving the scaling of the partition function. We also extend the models to include a pulling force between one end of the pair of paths, which competes with the attractive monomer-monomer interactions between the polymers.

### Stable Higgs mode in anisotropic quantum magnets

Low-energy excitations associated with the amplitude fluctuation of an order parameter in condensed matter systems can mimic the Higgs boson, an elementary particle in the standard model, and are dubbed as Higgs modes. Identifying the condensed-matter Higgs mode is challenging because it is known in many cases to decay rapidly into other low-energy bosonic modes, which renders the Higgs mode invisible. Therefore, it is desirable to find a way to stabilize the Higgs mode, which can offer an insight into the stabilization mechanism of the Higgs mode in condensed matter physics. In quantum magnets, magnetic order caused by spontaneous symmetry breaking supports transverse (magnons) and longitudinal (Higgs modes) fluctuations. When a continuous symmetry is broken, the Goldstone magnon mode generally has a lower excitation energy than the Higgs mode, causing a rapid decay of the latter. In this work, we show that a stable Higgs mode exists in anisotropic quantum magnets near the quantum critical point between the dimerized and magnetically ordered phases. We find that an easy axis anisotropy increases the magnon gap such that the magnon mode is above the Higgs mode near the quantum critical point, and the decay of the Higgs mode into the magnon mode is forbidden kinematically. Our results suggest that the anisotropic quantum magnets provide ideal platforms to explore the Higgs physics in condensed matter systems.

### A pure non-neutral plasma under an external harmonic field: equilibrium thermodynamics and chaos

Motivated by the precedent study of Ordenes-Huanca and Velazquez [JSTAT \textbf{093303} (2016)], we address the study of a simple model of a pure non-neutral plasma: a system of identical non-relativistic charged particles confined under an external harmonic field with frequency $\omega$. We perform the equilibrium thermo-statistical analysis in the framework of continuum approximation. This study reveals the existence of two asymptotic limits: the known Brillouin steady state at zero temperature, and the gas of harmonic oscillators in the limit of high temperatures. The non-extensive character of this model is evidenced by the associated thermodynamic limit, $N\rightarrow+\infty: U/N^{7/3}=const$, which coincides with the thermodynamic limit of a self-gravitating system of non-relativistic point particles in presence of Newtonian gravitation. Afterwards, the dynamics of this model is analyzed through numerical simulations. It is verified the agreement of thermo-statistical estimations and the temporal expectation values of the same macroscopic observables. The system chaoticity is addressed via numerical computation of Lyapunov exponents in the framework of the known \emph{tangent dynamics}. The temperature dependence of Lyapunov exponent $\lambda$ approaches to zero in the two asymptotic limits of this model, reaching its maximum during the transit between them. The chaos of the present model is very strong, since its rate is faster than the characteristic timescale of the microscopic dynamics $\tau_{dyn}=1/\omega$. A qualitative analysis suggests that such a strong chaoticity cannot be explained in terms of collision events because of their respective characteristic timescales are quite different, $\tau_{ch}\propto \tau_{dyn}/N^{1/4}$ and $\tau_{coll}\propto \tau_{dyn}$.

### On the coarsening mechanism and deformation of borides under annealing and creep in a polycrystalline superalloy

We have investigated the coarsening mechanism of intergranular Cr-rich M2B borides after creep and annealing at 850C for approximately 3000 hours in a polycrystalline nickel-based superalloy. Borides were found to be coarser after creep, with measured thicknesses in the range of 800-1100nm, compared to borides annealed in the absence of external applied load (400-600nm). The borides had a thickness of 100-200nm before exposure at 850C. Transmission electron microscopy revealed that coarsened borides have either the tetragonal I4/mcm structure, or the orthorhombic Fddd, with those two structures coexisting in a single particle. The presence of a very high density of planar faults is systematically observed within the coarsened borides. The faults were correlated with chemical fluctuations of B and Cr, revealed by atom probe tomography. Our results allow us to suggest that borides coarsen by an epitaxy-like mechanism. In addition, partitioning of Ni and Co was observed at dislocations within the borides after creep providing insights into the deformation of borides. Consequences of coarsened intergranular borides on the creep performance of polycrystalline superalloys are discussed.

### Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices

We perform extensive classifications of $\mathbb{Z}_2$ quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices using a spin-rotation invariant fermionic projective symmetry group approach. Taking into account that all three lattices share the same point group $O_h$, we apply an efficient gauge where the classification for the simple cubic lattice can be partially carried over to the other two lattices. We identify hundreds of projective representations for each of the three lattices, however, when constructing short-range mean-field models for the fermionic partons (spinons) these phases collapse to only very few relevant cases. We self-consistently calculate the corresponding mean-field parameters for frustrated Heisenberg models on all three lattices with up to third neighbor spin interactions and discuss the spinon dispersions, ground state energies and dynamical spin structure factors. Our results indicate that phases with non-uniform spinon hopping or pairing amplitudes are energetically favored. An unusual situation is identified for the fcc lattice where the spinon dispersion minimizing the mean-field energy features a network of symmetry protected line-like zero modes in reciprocal space. We further discuss characteristic fingerprints of these phases in the dynamical spin structure factor which may help to identify and distinguish them in future numerical or experimental studies.

### Magnetoconductivity oscillations induced by intersubband excitation in a degenerate 2D electron gas

Magnetoconductivity oscillations and absolute negative conductivity induced by nonequilibrium populations of excited subbands in a degenerate multisubband two-dimensional electron system are studied theoretically. The displacement from equilibrium, which can be caused by resonant microwave excitation or by any other reason, is assumed to be such that electron distributions can no longer be described by a single Fermi level. In this case, in addition to the well-known conductivity peaks occurring at the Shubnikov-de Haas conditions and small peaks of normal intersubband scattering, sign-changing oscillations with a different shape are shown to be possible. We found also that even a small fraction of electrons transferred to the excited subband can lead to negative conductivity effects.

### Derivation of the density operator with quantum analysis for the generalized Gibbs ensemble in quantum statistics

We derived the equation of the density operator for generalized entropy and generalized expectation value with quantum analysis when conserved quantities exist. The derived equation is simplified when the conventional expectation value is employed. The derived equation is also simplified when the commutation relations, $[\hat{\rho}, \hat{H}]$ and $[\hat{\rho}, \hat{Q}^{[a]}]$, are the functions of the density operator $\hat{\rho}$, where $\hat{H}$ is the Hamiltonian, and $\hat{Q}^{[a]}$ is the conserved quantity. We derived the density operators for the von Neumann entropy, the Tsallis entropy, and the R\'enyi entropy in the case of the conventional expectation value. We also derived the density operators for the Tsallis entropy and the R\'enyi entropy in the case of the escort average (the normalized $q$-expectation value), when the density operator commutes with the Hamiltonian and the conserved quantities. We found that the argument of the density operator for the canonical ensemble is simply extended to the argument for the generalized Gibbs ensemble in the case of the conventional expectation value, even when conserved quantities do not commute. The simple extension of the argument is also shown in the case of the escort average, when the density operator $\hat{\rho}$ commutes with the Hamiltonian $\hat{H}$ and the conserved quantity $\hat{Q}^{[a]}$: $[\hat{\rho}, \hat{H}] = [\hat{\rho}, \hat{Q}^{[a]}]=0$. These findings imply that the argument of the density operator for the canonical ensemble is simply extended to the argument for the generalized Gibbs ensemble in some systems.

### Note on a Floquet/Bloch-band fusion phenomenon in scattering by truncated periodic multi-well potentials

A transmission phenomenon for a quantal particle scattered through a multi-well potential in one dimension is observed by means of an amplitude-phase method. The potential model consists of $N$ identical potential cells, each containing a symmetric well. Typical transmission bands contain $N-1$ possible energies of total transmission. It is found that certain band types contain $n$ energies of total transmission. A fusion phenomenon of this type of band with a typical neigboring band is also found. As the transmission gap between them collapse and disappear, a resulting fused single band is seen to contain $2N-1$ energy peaks of total transmission.

### Spin-canting effects in GMR sensors with wide dynamic field range

Magnetoresistive (xMR) sensors find extensive application in science and industry, replacing Hall sensors in various low field environments. While there have been some efforts in increasing the dynamic field range of xMR sensors, Hall sensors remain to dominate high field applications due to their wide linear range. Using a perpendicular magnetized reference system and an in-plane free layer allows us to overcome this disadvantage of xMR sensors, and, furthermore, investigate spin-canting effects in interlayer exchange coupled perpendicular synthetic antiferromagnets (p-SAF). We created p-SAFs with exchange coupling fields of up to 10 kOe, based on magnetic Co/Pt multilayer systems. The p-SAFs are either designed as "single" p-SAFs, where two Co/Pt multilayers are interlayer exchange coupled via a 4 {\AA} thick Ru spacer, or as "double" p-SAFs, where an additional Co layer is interlayer exchange coupled to the top multilayer. These p-SAFs are used for giant magnetoresistance (GMR) sensors with wide dynamic field range. By using a p-SAF as the reference system and employing an in-plane magnetic layer as the GMR's free layer, the linear range can be effectively increased limited only by the p-SAF's switching fields. Additionally, the magnetic anisotropy of the in-plane free layer is fully controlled, which allows saturation fields by design. Different configurations were investigated, ranging from free layer magnetic saturation at lower to far higher fields than the p-SAF's switching fields. We can show through micromagnetic simulations that certain GMR transfer curves are dominated by spin-canting effects in the interlayer exchange coupled reference system. Finally, our simulation results lay out the correlation of the p-SAF's design parameters and its magnetization reversal behavior.

### Hippopede curves for modelling radial spin waves in an azimuthal graded magnonic landscape

We propose a mathematical model for describing radially propagating spin waves emitted from the core region in a magnetic patch with n vertices in a magnetic vortex state. The azimuthal anisotropic propagation of surface spin waves (SSW) into the domain, and confined spin waves (or Winter's Magnons, WM) in domain walls increases the complexity of the magnonic landscape. In order to understand the spin wave propagation in these systems, we first use an approach based on geometrical curves called 'hippopedes', however it provides no insight into the underlying physics. Analytical models rely on generalized expressions from the dispersion relation of SSW with an arbitrary angle between magnetization M and wavenumber k. The derived algebraic expression for the azimuthal dispersion is found to be equivalent to that of the 'hippopede' curves. The fitting curves from the model yield a spin wave wavelength for any given azimuthal direction, number of patch vertices and excitation frequency, showing a connection with fundamental physics of exchange dominated surface spin waves. Analytical results show good agreement with micromagnetic simulations and can be easily extrapolated to any n-corner patch geometry.

### Elasticity, stability, and quasi-oscillations of cell-cell junctions in solid confluent epithelia

Macroscopic properties and shapes of biological tissues depend on remodelling of cell-cell junctions at the microscopic scale. We propose a theoretical framework that couples a vertex model of solid confluent tissues with the dynamics describing generation of local force dipoles in the junctional actomyosin. Depending on the myosin-turnover rate, junctions preserve stable length or collapse to initiate cell rearrangements. We find that while the elasticity of solid tissues does not meet the conditions for a stable limit cycle of junctional movements, junctional noise can amplify and sustain transient oscillations to the fixed point, yielding quasi-periodic junctional dynamics. We also discover that junctional stability is affected by cell arrangements and junctional rest tensions, which may explain junctional collapse during convergence and extension in embryos.

### Thermodynamics and screening in the Ising-Kondo model

We introduce and study a simplification of the symmetric single-impurity Kondo model. In the Ising-Kondo model, host electrons scatter off a single magnetic impurity at the origin whose spin orientation is dynamically conserved. This reduces the problem to potential scattering of spinless fermions that can be solved exactly using the equation-of-motion technique. The Ising-Kondo model provides an example for static screening. At low temperatures, the thermodynamics at finite magnetic fields resembles that of a free spin-1/2 in a reduced external field. Alternatively, the Curie law can be interpreted in terms of an antiferromagnetically screened effective spin. The spin correlations decay algebraically to zero in the ground state and display commensurate Friedel oscillations. In contrast to the symmetric Kondo model, the impurity spin is not completely screened, i.e., the screening cloud contains less than a spin-1/2 electron. At finite temperatures and weak interactions, the spin correlations decay to zero exponentially with correlation length $\xi(T)=1/(2\pi T)$.

### Microscopic Insight into the Electronic Structure of BCF-Doped Oligothiophenes from \textit{Ab initio} Many-Body Theory

Lewis acids like tris(pentafluorophenyl)borane (BCF) offer promising routes for efficient $p$-doping of organic semiconductors. The intriguing experimental results achieved so far call for a deeper understanding of the underlying doping mechanisms. In a first-principles work, based on state-of-the-art density-functional theory and many-body perturbation theory, we investigate the electronic and optical properties of donor/acceptor complexes formed by quarterthiophene (4T) doped by BCF. For reference, hexafluorobenzene (C$_6$F$_6$) and BF$_3$ are also investigated as dopants for 4T. Modelling the adducts as bimolecules \textit{in vacuo}, we find negligible charge transfer in the ground state and frontier orbitals either segregated on opposite sides of the interface (4T:BCF) or localized on the donor (4T:BF$_3$, 4T:C$_6$F$_6$). In the optical spectrum of 4T:BCF, a charge-transfer excitation appears at lowest-energy, corresponding to the transition between the frontier states, which exhibit very small but non-vanishing wave-function overlap. In the other two adducts, the absorption is given by a superposition of the features of the constituents. Our results clarify that the intrinsic electronic interactions between donor and acceptor are not responsible for the doping mechanisms induced by BCF and related Lewis acids. Extrinsic factors, such as solvent-solute interactions, intermolecular couplings, and thermodynamic effects, have to be systematically analyzed for this purpose.

### An Origin of Dzyaloshinskii-Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR Interaction

We present a theory of both the itinerant carrier-mediated RKKY interaction and the virtual excitations-mediated Bloembergen-Rowland (BR) interaction between magnetic moments in graphene induced by proximity effect with a ferromagnetic film. We show that the RKKY/BR interaction consists of the Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms. In the case of the nearest distance, we estimate the DM term from the RKKY/BR interaction is about 0.13 meV for the graphene/Co interface, which is consistent with the experimental result of DM interaction $0.16 \pm 0.05$ meV. Our calculations indicate that the intralayer RKKY/BR interaction may be a possible physical origin of the DM interaction in the graphene-ferromagnet interface. This work provides a new perspective to comprehend the DM interaction in graphene/ferromagnet systems.

### A semi-analytical model for the scale-dependent friction of nanosized asperity

The friction of a nanosized sphere in commensurate contact with a flat substrate is investigated by performing molecular dynamics simulations. Particular focus is on the distribution of shear stress within the contact region. It is noticed that within the slip zone, the local friction coefficient defined by the ratio of shear stress to normal pressure declines monotonically as the distance to contact center increases. With the lateral force increasing, the slip zone expands inwards from the contact edge. At the same time, the local friction coefficient at the contact edge decreases continuously, while at the dividing between the slip and stick zones keeps nearly invariant. These characteristics are distinctly different from the prediction of the conventional Cattaneo-Mindlin model assuming a constant local friction coefficient within the slip zone. An analytical model is advanced in view of such new features and generalized based on numerous atomic simulations. This model not only accurately characterizes the interfacial shear stress, but also explains the size-dependence of static friction of single nanosized asperity.

### Interface evolution in phase transformation ruled by nucleation and growth

An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations in 2D and 3D space and the latter nucleation and growth on flat solid substrate. The theory is formulated for the general case of spatially correlated nuclei, arbitrary nucleation rate and power growth law of nuclei. In the case of heterogeneous nucleation, spheroidal nuclei have been assumed and the dependence of the kinetics on contact angle investigated. The validity of the present approach is deemed through comparison with experimental data from literature which also comprise oxide growth by ALD (Atomic Layer Deposition) metal electrodeposition at solid substrate and alloy recrystallization.

### Consistent analytical solution for the response of a nanoscale circuit to a mode-locked laser

It is now common practice to solve the Schr\"odinger equation to estimate the tunneling current between two electrodes at specified potentials, or the transmission through a potential barrier by assuming that there is an incident, reflected, and transmitted wave. However, these two approaches may not be appropriate for applications with nanoscale circuits. A new approach is required because the electron man-free path may be as long as 68.2 nm in metals so it is possible that the wavefunction may be coherent throughout a nanoscale circuit. We define several algorithms for determining the eigenvalues with different sets of the circuit parameters, thus demonstrating the existence of consistent solutions for nanoscale circuits. We also present another algorithm that is being applied to determine the full solution for nanoscale circuits. All of this is done using only analytical solutions of the Schr\"odinger equation.

### Second and third harmonics generation by coherent sub-THz radiation at induced Lifshitz transitions in gapped bilayer graphene

Using the microscopic nonlinear quantum theory of interaction of strong coherent electromagnetic radiation with a gapped bilayer graphene is developed for high harmonic generation at low-energy photon excitation-induced Lifshitz transitions. The Liouville-von Neumann equation for the density matrix is solved numerically at the nonadiabatic multiphoton excitation regime. By numerical solutions, we examine the rates of the second and third harmonics generation at the particle-hole annihilation in induced Lifshitz transitions by the two linearly polarized coherent electromagnetic waves propagating in opposite directions. The obtained results show that the gapped bilayer graphene can serve as an effective medium for generation of even and odd high harmonics in the sub-THz domain of frequencies.

### An ES-BGK model for vibrational polyatomic gases

We propose an extension of the Ellipsoidal-Statistical BGK model to account for discrete levels of vibrational energy in a rarefied polyatomic gas. This model satisfies an H-theorem and contains parameters that allow to fit almost arbitrary values for the Prandtl number and the relaxation times of rotational and vibrational energies. With the reduced distribution technique , this model can be reduced to a three distribution system that could be used to simulate polyatomic gases with rotational and vibrational energy for a computational cost close to that of a simple monoatomic gas.

### Signatures of Long-Range Spin-Triplet Component in Andreev Interferometer

We analyze the Josephson,$I_{J}$, and dissipative,$I_{V}$, currents in a magnetic Andreev interferometer in the presence of the long-range spin triplet component (LRSTC). Andreev interferometer has a cross-like geometry and consists of a SF$_{l}$ - F - F$_{r}$S circuit and perpendicular to it a N - F - N circuit, where S, F$_{l,r}$ are superconductors and weak ferromagnets with non-collinear magnetisations $\mathbf{M}_{l,r}$, F is a strong ferromagnet. The ferromagnetic wire F can be replaced with a non-magnetic wire n. In the limit of a weak proximity effect (PE), we obtain simple analytical expressions for the currents $I_{J}$ and $I_{V}$. In particular, the critical Josephson current in a long Josephson junction (JJ) is $I_{c}(\alpha ,\beta )=I_{0c}\chi (\alpha ,\beta )$, where the function $% \chi (\alpha ,\beta )$ is a function of angles $(\alpha ,\beta )_{l,r}$ that characterize the orientations of $\mathbf{M}_{l,r}$. The oscillating part of the dissipative current $I_{osc}(V)=\chi (\alpha ,\beta )\cos \varphi I_{0}(V)$ in the N - F(n)- N circuit depends on the angles $(\alpha ,\beta )_{l,r}$ in the same way as the critical Josephson current $I_{c}(\alpha ,\beta )$, but can be much greater than the $I_{c}(\alpha ,\beta )$. At some angles the current $I_{c}(\alpha ,\beta )$ changes sign. We briefly discuss a relation between the negative current $I_{c}$ and paramagnetic response. We argue that the measurements of the conductance in N - F(n) - N circuit can be used as another complementary method to identify the LRSTC in S/F heterostructures.

### Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams

In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to any of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded green Dyadic, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.

### Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges

The most promising mechanisms for the formation of Majorana bound states (MBSs) in condensed matter systems involve one-dimensional systems (such as semiconductor nanowires, magnetic chains, and quantum spin Hall insulator (QSHI) edges) proximitized to superconducting materials. The choice between each of these options involves trade-offs between several factors such as reproducibility of results, system tunability, and robustness of the resulting MBS. In this article, we propose that a combination of two of these systems, namely a magnetic chain deposited on a QSHI edge in contact with a superconducting surface, offers a better choice of tunability and MBS robustness compared to magnetic chain deposited on bulk. We study how the QSHI edge interacts with the magnetic chain, and see how the topological phase is affected by edge proximity. We show that MBSs near the edge can be realized with lower chemical potential and Zeeman field than the ones inside the bulk, independently of the chain's magnetic order (ferromagnetic or spiral order). Different magnetic orderings in the chain modify the overall phase diagram, even suppressing the boundless topological phase found in the bulk for chains located at the QSHI edge. Moreover, we quantify the "quality" of MBSs by calculating the Majorana Polarization (MP) for different configurations. For chains located at the edge, the MP is close to its maximum value already for short chains. For chains located away from the edge, longer chains are needed to attain the same quality as chains located at the edge. The MP also oscillates in phase with the in-gap states, which is relatively unexpected as peaks in the energy spectrum corresponds to stronger overlap of MBSs.

### Electro-mechanically guided growth and patterns

Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and capture some growth phenomena found in Nature, we extend volume growth theory to account for an electro-elasticity coupling. Based on the multiplicative decomposition, we present a general analysis of isotropic growth and pattern formation of electro-elastic solids under external mechanical and electrical fields. As an example, we treat the case of a tubular structure to illustrate an electro-mechanically guided growth affected by axial strain and radial voltage. Our numerical results show that a high voltage can enhance the non-uniformity of the residual stress distribution and induce extensional buckling, while a low voltage can delay the onset of wrinkling shapes and can also generate more complex morphologies. Within a controllable range, axial tensile stretching shows the ability to stabilise the tube and help form more complex 3D patterns, while compressive stretching promotes instability. Both the applied voltage and external axial strain have a significant impact on guiding growth and pattern formation. Our modelling provides a basic tool for analysing the growth of electro-elastic materials, which can be useful for designing a pattern prescription strategy or growth self-assembly in Engineering.

### Spectral properties of heterostructures containing half-metallic ferromagnets in the presence of local many-body correlations

In this work, we investigate models for bulk, bi- and multilayers containing half-metallic ferromagnets (HMFs), at zero and at finite temperature, in order to elucidate the effects of strong electronic correlations on the spectral properties (density of states). Our focus is on the evolution of the finite-temperature many-body induced tails in the half-metallic gap. To this end, the dynamical mean-field theory (DMFT) is employed. For the bulk, a Bethe lattice model is solved using a matrix product states based impurity solver at zero temperature and a continuous-time quantum Monte Carlo (CT-QMC) solver at finite temperature. We demonstrate numerically, in agreement with the analytical result, that the tails vanish at the Fermi level at zero temperature. In order to study multilayers, taken to be square lattices within the layers, we use the real-space DMFT extension with the CT-QMC impurity solver. For bilayers formed by the HMF with a band or correlated insulator, we find that charge fluctuations between the layers enhance the finite temperature tails. In addition, in the presence of inter-layer hopping, a coherent quasiparticle peak forms in the otherwise correlated insulator. In the multilayer heterostructure setup, we find that by suitably choosing the model parameters, the tails at the HMF/Mott insulator interface can be reduced significantly, and that a high spin polarization is conceivable, even in the presence of long-ranged electrostatic interactions.

### Interaction induced point scatterer lattices and flat band condensation of exciton-polaritons

One of the recently established paradigms in the study of condensed matter physics is examining a system's behaviour in artificially constructed potentials. This allows one to obtain insight on a range of physical phenomena which may require non-feasible or hardly achievable experimental conditions. Here, we devise and implement an all-optical approach to a system of exciton-polaritons in semiconductor microcavities to load the particles into desired periodic potentials. We demonstrate a two-dimensional system of polariton condensates in two regimes - lattices of point scatterers, and confined states through non-resonant pumping with Gaussian beams arranged in a conventional, and an inverse Lieb configuration. We utilize energy tomography on the coherent polariton emission to reveal the intricate band structure of polaritonic Lieb lattices, and report on fully optically generated polariton condensation in S-, and dispersionless P-band states.

### Spin-flip excitations and Stoner ferromagnetism in a strongly correlated quantum Hall system

Spin-flip excitations in a quantum Hall electron system at fixed filling factor nu=2 are modelled and studied under conditions of a strong Coulomb interaction when the Landau level mixing' is a dominant factor determining the excitation energy. The one-exciton' approach used for the purely electronic excitations in question allows us to describe the Stoner transition from the unpolarized/paramgnet state to the polarized/ferromagnet one. The theoretical results are compared with the available experimental data.

### Predicting the properties of metachronal waves from single-cilium characteristics

On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of individual cilia to the collective dynamics of a ciliary carpet via systematic coarse-graining. We uncover the criteria that control the selection of frequency and wavevector of stable metchacronal waves and examine how they depend on the geometric and dynamical characteristics of single cilia, as well as the geometric properties of the array. Our results can contribute to understanding how the collective properties of ciliary arrays can be controlled, which can have significant biological, medical, and engineering implications.

### Tolerance versus synaptic noise in dense associative memories

The retrieval capabilities of associative neural networks can be impaired by different kinds of noise: the fast noise (which makes neurons more prone to failure), the slow noise (stemming from interference among stored memories), and synaptic noise (due to possible flaws during the learning or the storing stage). In this work we consider dense associative neural networks, where neurons can interact in $p$-plets, in the absence of fast noise, and we investigate the interplay of slow and synaptic noise. In particular, leveraging on the duality between associative neural networks and restricted Boltzmann machines, we analyze the effect of corrupted information, imperfect learning and storing errors. For $p=2$ (corresponding to the Hopfield model) any source of synaptic noise breaks-down retrieval if the number of memories $K$ scales as the network size. For $p>2$, in the relatively low-load regime $K \sim N$, synaptic noise is tolerated up to a certain bound, depending on the density of the structure.

### Transverse and Longitudinal Spin-Torque Ferromagnetic Resonance for Improved Measurements of Spin-Orbit Torques

Spin-torque ferromagnetic resonance (ST-FMR) is a common method used to measure spin-orbit torques (SOTs) in heavy metal/ferromagnet bilayer structures. In the course of a measurement, other resonant processes such as spin pumping (SP) and heating can cause spin current or heat flows between the layers, inducing additional resonant voltage signals via the inverse spin Hall effect (ISHE) and Nernst effects (NE). In the standard ST-FMR geometry, these extra artifacts exhibit a dependence on the angle of an in-plane magnetic field that is identical to the rectification signal from the SOTs. We show experimentally that the rectification and artifact voltages can be quantified separately by measuring the ST-FMR signal transverse to the applied current (i.e., in a Hall geometry) in addition to the usual longitudinal geometry. We find that in Pt (6 nm)/CoFeB samples the contribution from the artifacts is small compared to the SOT rectification signal for CoFeB layers thinner than 6 nm, but can be significant for thicker magnetic layers. We observe a sign change in the artifact voltage as a function of CoFeB thickness that we suggest may be due to a competition between a resonant heating effect and the SP/ISHE contribution.

### Propulsion and energetics of a minimal magnetic microswimmer

In this manuscript we describe the realization of a minimal hybrid microswimmer, composed of a ferromagnetic nanorod and a paramagnetic microsphere. The unbounded pair is propelled in water upon application of a swinging magnetic field that induces a periodic relative movement of the two composing elements, where the nanorod rotates and slides on the surface of the paramagnetic sphere. When taken together, the processes of rotation and sliding describe a finite area in the parameter space, which increases with the frequency of the applied field. We develop a theoretical approach and combine it with numerical simulations, which allow us to understand the dynamics of the propeller and explain the experimental observations. Furthermore, we demonstrate a reversal of the microswimmer velocity by varying the length of the nanorod, as predicted by the model. Finally, we determine theoretically and in experiments the Lighthill's energetic efficiency of this minimal magnetic microswimmer.

### Micro-slips inside a granular shear band as nano-earthquakes

We study experimentally the fluctuations of deformation along a shear fault naturally emerging within a compressed frictional granular medium. Using laser interferometry, we show that the deformation inside this granular gouge occurs as a succession of localized micro-slips distributed along the fault. The associated distributions of released seismic moments, the memory effects in strain fluctuations, as well as the time correlations between successive events, follow exactly the empirical laws of natural earthquakes. Using a methodology initially developed in seismology and social science, we reveal, for the first time at the laboratory scale, the underlying causal structure. This demonstrates that the spatio-temporal correlations of the slip dynamics effectively emerge from more fundamental triggering kernels. This formal analogy between natural faults and our experimentally controllable granular shear band opens the way towards a better understanding of earthquake physics. In particular, comparing experiments performed under different imposed deformation rates, we show that strain, not time, is the right parameter controlling the memory effects in the dynamics of our fault analog. This raises the fundamental question of the relative roles of strain-dependent structural rearrangements within the fault gouge vs that of truly time-dependent, thermally activated processes, in the emergence of spatio-temporal correlations of natural seismicity.

### Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy

We study the phase diagram of spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power-law $\propto r^{-\alpha}$ ($\alpha\ge 1$) accompanied by modulated single-ion anisotropy. Employing the techniques of the density-matrix renormalization group, effects of long-range interactions and single-ion anisotropy on a variety of correlations are investigated. In order to check the consistency, the fidelity susceptibilities are evaluated across quantum phase transitions. The quantum critical points are faithfully detected and orders of phase transitions are determined. The correlation-length critical exponent is extracted from scaling functions of the fidelity susceptibility. The presence of long-range interactions leads to quantitative change of the phase boundaries and reduces the order of phase transition under certain conditions. A direct first-order transition between the periodic N\'eel phase and the large-$D$ phase occurs for slowly decaying antiferromagnetic interactions.

### The spontaneous symmetry breaking in Ta$_2$NiSe$_5$ is structural in nature

The excitonic insulator is an electronically-driven phase of matter that emerges upon the spontaneous formation and Bose condensation of excitons. Detecting this exotic order in candidate materials is a subject of paramount importance, as the size of the excitonic gap in the band structure establishes the potential of this collective state for superfluid energy transport. However, the identification of this phase in real solids is hindered by the coexistence of a structural order parameter with the same symmetry as the excitonic order. Only a few materials are currently believed to host a dominant excitonic phase, Ta$_2$NiSe$_5$ being the most promising. Here, we test this scenario by using an ultrashort laser pulse to quench the broken-symmetry phase of this transition metal chalcogenide. Tracking the dynamics of the material's electronic and crystal structure after light excitation reveals surprising spectroscopic fingerprints that are only compatible with a primary order parameter of phononic nature. We rationalize our findings through state-of-the-art calculations, confirming that the structural order accounts for most of the electronic gap opening. Not only do our results uncover the long-sought mechanism driving the phase transition of Ta$_2$NiSe$_5$, but they also conclusively rule out any substantial excitonic character in this instability.

### New Recipes for Brownian Loop Soups

We define a large new class of conformal primary operators in the ensemble of Brownian loops in two dimensions known as the Brownian loop soup,'' and compute their correlation functions analytically and in closed form. The loop soup is a conformally invariant statistical ensemble with central charge $c = 2 \lambda$, where $\lambda > 0$ is the intensity of the soup. Previous work identified exponentials of the layering operator $e^{i \beta N(z)}$ as primary operators. Each Brownian loop was assigned $\pm 1$ randomly, and $N(z)$ was defined to be the sum of these numbers over all loops that encircle the point $z$. These exponential operators then have conformal dimension ${\frac{\lambda}{10}}(1 - \cos \beta)$. Here we generalize this procedure by assigning a more general random value to each loop. The operator $e^{i \beta N(z)}$ remains primary with conformal dimension $\frac {\lambda}{10}(1 - \phi(\beta))$, where $\phi(\beta)$ is the characteristic function of the probability distribution used to assign random values to each loop. Using recent results we compute in closed form the exact two-point functions in the upper half-plane and four-point functions in the full plane of this very general class of operators. These correlation functions depend analytically on the parameters $\lambda, \beta_i, z_i$, and on the characteristic function $\phi(\beta)$. They satisfy the conformal Ward identities and are crossing symmetric. As in previous work, the conformal block expansion of the four-point function reveals the existence of additional and as-yet uncharacterized conformal primary operators.

### Quantum fluctuations hinder finite-time information erasure near the Landauer limit

Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow driving limit, we prove that coherence provides a non-negative contribution to all statistical cumulants. Using the simple and paradigmatic example of single bit erasure, we show that these extreme dissipation events yield distinct, experimentally distinguishable signatures.

### Novel Memory Structures in QCA Nano Technology

Quantum-dot Cellular Automata (QCA) is a new emerging technology for designing electronic circuits in nanoscale. QCA technology comes to overcome the CMOS limitation and to be a good alternative as it can work in ultra-high-speed. QCA brought researchers attention due to many features such as low power consumption, small feature size in addition to high frequency. Designing circuits in QCA technology with minimum costs such as cells count and the area is very important. This paper presents novel structures of D-latch and D-Flip Flop with the lower area and cell count. The proposed Flip-Flop has SET and RESET ability. The proposed latch and Flip-Flop have lower complexity compared with counterparts in terms of cell counts by 32% and 26% respectively. The proposed circuits are designed and simulated in QCADesigner software.

### Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks

Curie's principle states that "when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them". We demonstrate that symmetry equivariant neural networks uphold Curie's principle and this property can be used to uncover symmetry breaking order parameters necessary to make input and output data symmetrically compatible. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry breaking input to deform a square into a rectangle.

### Relationship between manifold smoothness and adversarial vulnerability in deep learning with local errors

Artificial neural networks can achieve impressive performances, and even outperform humans in some specific tasks. Nevertheless, unlike biological brains, the artificial neural networks suffer from tiny perturbations in sensory input, under various kinds of adversarial attacks. It is therefore necessary to study the origin of the adversarial vulnerability. Here, we establish a fundamental relationship between geometry of hidden representations (manifold perspective) and the generalization capability of the deep networks. For this purpose, we choose a deep neural network trained by local errors, and then analyze emergent properties of trained networks through the manifold dimensionality, manifold smoothness, and the generalization capability. To explore effects of adversarial examples, we consider independent Gaussian noise attacks and fast-gradient-sign-method (FGSM) attacks. Our study reveals that a high generalization accuracy requires a relatively fast power-law decay of the eigen-spectrum of hidden representations. Under Gaussian attacks, the relationship between generalization accuracy and power-law exponent is monotonic, while a non-monotonic behavior is observed for FGSM attacks. Our empirical study provides a route towards a final mechanistic interpretation of adversarial vulnerability under adversarial attacks.

### Expulsion from structurally balanced paradise

We perform simulations of structural balance evolution on a triangular lattice using the heat-bath algorithm. In contrast to similar approaches -- but applied to analysis of complete graphs -- the triangular lattice topology successfully prevents the occurrence of even partial Heider's balance. Starting with the state of Heider's paradise, it is just a matter of time when the evolution of the system leads to an unbalanced and disordered state. The time of the system relaxation does not depend on the system size. The lack of any signs of balanced state was not observed in earlier investigated systems dealing with structural balance

### High Entropy Alloys as a new metaphor in sociophysics

Most of the opinion dynamics models in sociophysics have their historic origin in studies two-dimensional magnetization phenomena. This metaphor has proven quite useful, as it allowed to use well known techniques, relating individual behaviours of single spins and their interactions, to large scale properties, such as magnetization or magnetic domains creation. These physical properties were then mapped'' to social concepts: spin orientation to a person's views on a specific issue, magnetization to global opinion on the issue, etc. During the past 20 years, the models were significantly expanded, using more complex individual agent characteristics and even more complex types of the interactions, but the power of the metaphor remained unchanged. In the current paper we propose to use a new physical system as the basis for new ideas in sociophysics. We shall argue that the concepts and tools devoted to studies of High Entropy Alloys (HEAs) could significantly broaden the range of social concepts addressable'' by sociophysics, by focusing on a wider range of global phenomena, arising from atomic properties, interactions and arrangements. We illustrate the new idea by calculating a few characteristics of a simple HEA system and their possible `mapping'' into social concepts.

### Generation and dynamics of entangled fermion-photon-phonon states in nanocavities

We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tri-state entanglement are realized near the parametric resonances in a coupled system. The model includes decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg-Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables, and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

### Robust Preparation of Many-body Ground States in Jaynes-Cummings Lattices

Strongly-correlated polaritons in Jaynes-Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and the superfluid phases at integer fillings. Here we present an approach for the robust preparation of many-body ground states of polaritons in a finite-sized JC lattice by optimized nonlinear ramping. In the deep Mott-insulating and deep superfluid regimes, polaritons can be pumped into a JC lattice and be prepared in the ground state with high accuracy via engineered pulse sequences. Using such states as initial state and employing optimized nonlinear ramping, we demonstrate that many-body ground states in the intermediate regimes of the parameter space can be generated with high fidelity. We exploit a Landau-Zener-type of estimation on this finite-sized system and derive an optimal ramping index for selected ramping trajectories, which greatly improves the fidelity of the prepared states. With numerical simulation of the ramping process, we further show that by choosing an appropriate trajectory, the fidelity can remain close to unity in almost the entire parameter space. This method is general and can be applied to many other systems.

### Quantum magnetic monopole condensate

Despite the decades-long efforts, magnetic monopoles were never found as elementary particles. Monopoles and associated currents were directly measured in experiments and identified as topological quasiparticle excitations in emergent condensed matter systems. These monopoles and the related electric-magnetic symmetry were restricted to classical electrodynamics, with monopoles behaving as classical particles. Here we show that the electric-magnetic symmetry is most fundamental and extends to full quantum behavior. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate dual to the charge Cooper pair condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. The monopole supercurrents result in the electric analog of the Meissner effect and lead to linear confinement of the Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons.

### Charge-voltage relation for a fractional capacitor

Most capacitors of practical use deviate from the assumption of a constant capacitance. They exhibit memory and are often described by a time-varying capacitance. It is shown that a direct implementation of the classical relation, $Q\left(t\right)=CV\left(t\right)$, that relates the charge, $Q\left(t\right)$, with the constant capacitance, $C$, and the voltage, $V\left(t\right)$, is not applicable when the capacitance is time-varying. The resulting equivalent circuit that emerges from the substitution of, $C$, by, $C\left(t\right)$, is found to be inconsistent. Since, $C\left(t\right)$, leads to a time-variant system, the current, $\dot{Q}$, that is obtained from the product rule of the differentiation is not valid either. The search for a solution to this problem led to the expression for the charge, that is given by the convolution of the time-varying capacitance with the first-order derivative of the voltage, as, $Q\left(t\right)=C\left(t\right)\ast\dot{V}\left(t\right)$. Coincidentally, this equation also corresponds to the charge-voltage relation for a fractional-capacitor which is probably \textit{first} reported in this Letter.

### A substrateless, flexible, and water-resistant organic light-emitting diode

Despite widespread interest, ultrathin and highly flexible light-emitting devices that can be seamlessly integrated and used for flexible displays, wearables, and as bioimplants remain elusive. Organic light-emitting diodes (OLEDs) with $\mu$m-scale thickness and exceptional flexibility have been demonstrated but show insufficient stability in air and moist environments due to a lack of suitable encapsulation barriers. Here, we demonstrate an efficient and stable OLED with a total thickness of $\approx$12 $\mu$m that can be fully immersed in water or cell nutrient media for weeks without suffering substantial degradation. The active layers of the device are embedded between conformal barriers formed by alternating layers of parylene-C and metal oxides that are deposited through a low temperature chemical vapour process. These barriers also confer stability of the OLED to repeated bending and to extensive postprocessing, e.g. via reactive gas plasmas, organic solvents, and photolithography. This unprecedented robustness opens up a wide range of novel possibilities for ultrathin OLEDs.

### On quantum bound states in equiperiodic multi-well potentials I: $-$ Locally periodic potential sequences and Floquet/Bloch bands

Two connected equiperiodic one-dimensional multi-well potentials of different well depths are studied. Floquet/Bloch energy bands for respective multi-well potential are found to be relevant for understanding level structures. Althoug energies are classically allowed in both multi-well potentials, a band gap of one multi-well potential makes this potential quantum-mechanically 'forbidden'. All energy levels are located in the union of the band regions.

### Efficient excitations and spectra within a perturbative renormalization approach

We present a self-consistent approach for computing the correlated quasiparticle spectrum of charged excitations in iterative $\mathcal{O}[N^5]$ computational time. This is based on the auxiliary second-order Green's function approach [O. Backhouse \textit{et al.}, JCTC (2020)], in which a self-consistent effective Hamiltonian is constructed by systematically renormalizing the dynamical effects of the self-energy at second-order perturbation theory. From extensive benchmarking across the W4-11 molecular test set, we show that the iterative renormalization and truncation of the effective dynamical resolution arising from the $2h1p$ and $1h2p$ spaces can substantially improve the quality of the resulting ionization potential and electron affinity predictions compared to benchmark values. The resulting method is shown to be superior in accuracy to similarly scaling quantum chemical methods for charged excitations in EOM-CC2 and ADC(2), across this test set, while the self-consistency also removes the dependence on the underlying mean-field reference. The approach also allows for single-shot computation of the entire quasiparticle spectrum, which is applied to the benzoquinone molecule and demonstrates the reduction in the single-particle gap due to the correlated physics, and gives direct access to the localization of the Dyson orbitals.

### Scalable Gaussian Processes for Predicting the Properties of Inorganic Glasses with Large Datasets

Gaussian process regression (GPR) is a useful technique to predict composition--property relationships in glasses as the method inherently provides the standard deviation of the predictions. However, the technique remains restricted to small datasets due to the substantial computational cost associated with it. Here, using a scalable GPR algorithm, namely, kernel interpolation for scalable structured Gaussian processes (KISS-GP) along with massively scalable GP (MSGP), we develop composition--property models for inorganic glasses based on a large dataset with more than 100,000 glass compositions, 37 components, and nine important properties, namely, density, Young's, shear, and bulk moduli, thermal expansion coefficient, Vickers' hardness, refractive index, glass transition temperature, and liquidus temperature. Finally, to accelerate glass design, the models developed here are shared publicly as part of a package, namely, Python for Glass Genomics (PyGGi).

### Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning

Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($\varphi$), permeability $k$, and tortuosity ($T$). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. It is demonstrated that the CNNs are able to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between $T$ and $\varphi$ has been reproduced and compared with the empirical estimate. The analysis has been performed for the systems with $\varphi \in (0.37,0.99)$ which covers five orders of magnitude span for permeability $k \in (0.78, 2.1\times 10^5)$ and tortuosity $T \in (1.03,2.74)$.

### Removal and Recovery of Ammonia from Wastewater using Ti$_3$C$_2$T$_x$ MXenes in Flow Electrode Capacitive Deionization

Flow electrode CDI systems (FE-CDI) have recently garnered attention because of their ability to prevent cross contamination, and operate in uninterrupted cycles ad infinitum. Typically, FE-CDI electrodes suffer from low conductivity, which reduces deionization performance. Higher mass loading to combat low conductivity leads to poor rheological properties, which prevent the process from being continuous and scalable. Herein, Ti3C2Tx MXenes were introduced as 1 mg/mL slurry electrodes in an FE-CDI system for the removal and recovery of ammonia from stimulated wastewater. The electrode performance was evaluated by operating the FE-CDI system with a feed solution of 500 mg/L NH4Cl running in batch mode at a constant voltage of 1.2 and -1.2 V in charging and discharging modes respectively. Despite low loading compared to activated carbon solution, Ti3C2Tx flowing electrodes showed markedly improved performance by achieving 60% ion removal efficiency in a saturation time of 115 minutes, and an unprecedented adsorption capacity of 460 mg/g. The system proved to be a green technology by exhibiting satisfactory charge efficiency of 58-70% while operating at a relatively low energy consumption of 0.45 kWh/kg when compared to the current industry standard nitrification-denitrification ammonia stripping process. A 92% regeneration efficiency showed that the electrodes were stable and suitable for long term and scalable usage. The results demonstrate that MXenes hold great potential in improving the FE-CDI process for energy-efficient removal and recovery of ammonium ions from wastewater.

### Non-Markovianity of Quantum Brownian Motion

We study quantum non-Markovian dynamics of the Caldeira-Leggett model, a prototypical model for quantum Brownian motion describing a harmonic oscillator linearly coupled to a reservoir of harmonic oscillators. Employing the exact analytical solution of this model one can determine the size of memory effects for arbitrary couplings, temperatures and frequency cutoffs. Here, quantum non-Markovianity is defined in terms of the flow of information between the open system and its environment, which is quantified through the Bures metric as distance measure for quantum states. This approach allows us to discuss quantum memory effects in the whole range from weak to strong dissipation for arbitrary Gaussian initial states. A comparison of our results with the corresponding results for the spin-boson problem show a remarkable similarity in the structure of non-Markovian behavior of the two paradigmatic models.

### Stokes flow due to point torques and sources in a spherical geometry

Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of known solutions by deriving the flow expressions due to a general point torque and point source in the presence of a stationary sphere with either a no-slip or a stress-free (no shear) boundary condition. For an axisymmetric point torque and a no-slip sphere the image system simplifies to a single image point torque, reminiscent of the solution for a point charge outside an equipotential sphere in electrostatics. By symmetry, this also gives a simple representation of the solution due to an axisymmetric point torque inside a rigid spherical shell. In all remaining cases, the solution can be described by a collection of physically intuitive point and line singularities. Our results will be useful for the theoretical modelling of the propulsion of microswimmers and efficient numerical implementation of far-field hydrodynamic interactions in this geometry.