Understanding the nature of Cooper pairs is essential to describe the properties of superconductors. The original proposal of Bardeen, Cooper, and Schrieffer (BCS) was based on electrons pairing with same energy and zero center-of-mass momentum. With the advent of new superconductors, different forms of pairing have been discussed. In particular, Cooper pairs with finite center-of-mass momentum have received large interest. Along with such finite-momentum pairs, pairing of electrons at different energies is also central to understanding some superconductors. Here, we investigate the interplay of finite-momentum and finite-energy Cooper pairs considering two different systems: a conventional $s$-wave superconductor under applied magnetic field and a $d$-wave finite-momentum pairing state in the absence of magnetic field. Investigating both these systems, we find finite-energy pairs persisting independently of finite-momentum pairing, and that they lead to odd-frequency superconducting correlations. We contrast this finding by showing that the even-frequency correlations are predominantly driven by zero-energy pairs. We further calculate the Meissner effect and find that odd frequency correlations are essential for correctly describing the Meissner effect.

We study the fluctuations responsible for pairing in the $d$-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum and frequency dependent fluctuations generate the $d-$wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity both in the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin-fluctuation theory.

The electric and chiral current response to the time and coordinate dependent pseudoelectric field $\mathbf{E}_5$ in Weyl semimetals is studied. It is found that $\mathbf{E}_5$ leads to an electric current in the direction perpendicular to the field and the wave vector of the perturbation. We dubbed this effect the anomalous pseudo-Hall effect. The response of the chiral or valley current to the pseudoelectric field is also found to be nontrivial. Since the wave vector for $\mathbf{E}_5$ cannot be neglected, the frequency profile of the chiral conductivity is drastically different from its electric counterpart showing a step-like feature instead of a smooth Drude peak. The proposed effects can be investigated by driving sound waves in Weyl semimetals with broken time-reversal symmetry.

Conservation laws and hydrodynamic transport can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher R\'enyi entropies. Here, we introduce a class of long-range random Clifford circuits with U$(1)$ symmetry, which act as minimal models for more generic quantum systems and provide an ideal framework toexplore this phenomenon. Depending on the exponent $\alpha$ controlling the probability $\propto r^{-\alpha}$ of gates spanning a distance $r$, transport in such circuits varies from diffusive to superdiffusive and then to superballistic. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to $S(t) \propto t^{1/z}$, where $z$ is the $\alpha$-dependent dynamical transport exponent. We explain this finding in terms of the inhibited operator spreading in U$(1)$-symmetric Clifford circuits, where the emerging light cones are intimately related to the transport behavior and are significantly narrower compared to circuits without conservation law. For sufficiently small $\alpha$, we show that the presence of hydrodynamic modes becomes irrelevant such that $S(t)$ behaves similarly in circuits with and without conservation law. Our work sheds light on the interplay of transport and entanglement and emphasizes the usefulness of constrained Clifford circuits to explore questions in quantum many-body dynamics.

We study the phase diagram of $\nu_e=7/3$ state in the $N=1$ Landau level in the presence of band mass anisotropy. Using density matrix renormalization group on an infinite cylinder geometry, we find a continuous transition from the topologically ordered Laughlin fractional quantum Hall state to a stripe phase with a period of approximately five and a half magnetic lengths. The transition is driven by the condensation of the magnetoroton mode which becomes gapless at the critical point. We interpret the transition within the composite-boson theory as the onset of stripe order in a superfluid background resulting from the roton mode going soft.

The family of AV$_3$Sb$_5$ (A = K, Rb, Cs) kagome metals exhibit charge density wave (CDW) order, proposed to be chiral, followed by a lower temperature superconducting state. Recent studies have proposed the importance of band structure saddle points proximal to the Fermi energy in governing these two transitions. Here we show the effects of hole-doping achieved via chemical substitution of Sn for Sb on the CDW and superconducting states in both KV$_3$Sb$_5$ and RbV$_3$Sb$_5$, and generate a phase diagram. Hole-doping lifts the $\Gamma$ pocket and van Hove singularities (vHs) toward $E_F$ causing the superconducting $T_C$ in both systems to increase to about 4.5 K, while rapidly suppressing the CDW state.

Here we assess the applicability of graph neural networks (GNNs) for predicting the grain-scale elastic response of polycrystalline metallic alloys. Using GNN surrogate models, grain-averaged stresses during uniaxial elastic tension in Low Solvus High Refractory (LSHR) Ni Superalloy and Ti 7wt%Al (Ti-7Al), as example face centered cubic and hexagonal closed packed alloys, are predicted. A transfer learning approach is taken in which GNN surrogate models are trained using crystal elasticity finite element method simulations and then the trained surrogate models are used to predict the mechanical response of microstructures measured using high-energy X-ray diffraction microscopy. The performance of using various microstructural and micromechanical descriptors for input nodal features to the GNNs is explored. The effects of elastic anisotropy on GNN model performance and outlooks for extension of the framework are discussed.

Poly(N-isopropylacrylamide)-based microgels are soft colloids undergoing a Volume Phase Transition (VPT) close to ambient temperature. Although widely employed for fundamental research and application purposes, the modifications of the microgels internal structure occurring at the VPT are not yet completely understood, especially concerning the role of electrostatics. Here we study in detail, both experimentally and numerically, the effect of the addition of acrylic acid (AAc) co-monomer on the microgel deswelling process. By combining viscosimetry, light scattering and electrophoresis, we show that the progressive addition of AAc increases the microgel mass and suppresses the occurrence of the VPT, progressively shifting the microgel collapse to higher temperatures. Most importantly, it also highly enhances the two-step deswelling of these submicron-sized networks, so that the inner core collapses at temperatures always lower than those marking the transition of the outer corona. These results indicate that a net increase of the charge density mismatch between the bulk and the surface of the microgels takes place. Numerical simulations fully confirm this scenario and clarify the impact of the charge distribution on the two-step deswelling, with mobile counterions efficiently screening the charges within the inner core, while leaving more monomers ionized on the surface. Our work unambiguously shows how electrostatic interactions influence the behavior of thermosensitive microgels in aqueous environment close to the VPT.

We investigated the electrostatic behavior of ferroelectric liquid droplets exposed to the pyroelectric field of a lithium niobate ferroelectric crystal substrate. The ferroelectric liquid is a nematic liquid crystal in which almost complete polar ordering of the molecular dipoles generates an internal macroscopic polarization locally collinear to the mean molecular long axis. Upon entering the ferroelectric phase by reducing the temperature from the nematic phase, the liquid crystal droplets become electromechanically unstable and disintegrate by the explosive emission of fluid jets. These jets are mostly interfacial, spreading out on the substrate surface, and exhibit fractal branching out into smaller streams to eventually disrupt, forming secondary droplets. We understand this behavior as a manifestation of the Rayleigh instability of electrically charged fluid droplets, expected when the electrostatic repulsion exceeds the surface tension of the fluid. In this case the charges are due to the bulk polarization of the ferroelectric fluid which couples to the pyroelectric polarization of the underlying lithium niobate substrate through its fringing field and solid-fluid interface coupling. Since the ejection of fluid does not neutralize the droplet surfaces, they can undergo multiple explosive events as the temperature decreases.

Molecular polaritons are hybrid light-matter states that emerge when a molecular transition strongly interacts with photons in a resonator. At optical frequencies, this interaction unlocks a way to explore and control new chemical phenomena at the nanoscale. Achieving such a control at ultrafast timescales, however, is an outstanding challenge, as it requires a deep understanding of the dynamics of the collectively coupled molecular excitation and the nanoconfined electromagnetic fields. Here, we investigate the dynamics of collective polariton states, realized by coupling molecular photoswitches to optically anisotropic plasmonic nanoantennas. Pump-probe experiments reveal an ultrafast collapse of polaritons to a single-molecule transition triggered by femtosecond-pulse excitation at room-temperature. Through a synergistic combination of experiments and quantum mechanical modelling, we show that the response of the system is governed by intramolecular dynamics, occurring one order of magnitude faster with respect to the unperturbed excited molecule relaxation to the ground state.

We discuss contributions to the thermopower in an electron fluid. A simple argument based on Newton's second law with the pressure gradient as the force suggests that the thermopower is given by a thermodynamic derivative, viz., the entropy per particle, rather than being an independent transport coefficient. The resolution is the existence of an entropic force that results from a coupling between the mass current and the heat current in the fluid. We also discuss and clarify some aspects of a recent paper (Phys. Rev. B {\bf 102}, 214306 (2020)) that provided a method for exactly solving electronic transport equations in the low-temperature limit.

The celebrated Wiedemann-Franz (WF) law which governs the relation between charge and heat transport traces back to the experimental discovery in 1853 by Wiedemann and Franz. Despite the fundamental difference of the quantum-statistical properties between fermions and bosons, the linear-in-$T$ behavior of the WF law at low temperatures has recently been found to be the universal property by the discovery of the WF law for magnon transport. However, the WF law is for the linear response, and whether or not the universal law is valid even in the nonlinear regime of Bose systems remains an open issue. Here we provide a solution to this fundamental challenge. We show that the ratio of the thermal to spin transport coefficient of magnons in topologically trivial insulating magnets exhibits a different behavior from the linear response and the universal law breaks down in the strong nonlinear regime. This finding is within experimental reach with current device and measurement technologies. Our discovery is the key ingredient in magnon-based spintronics, in the evaluation of the figure of merit for thermomagnetic conversion elements of spintronics devices.

Vortex fluctuations above and below the critical Kosterlitz-Thouless (KT) transition temperature are characterized using simulations of the 2D XY model. The net winding number of vortices at a given temperature in a circle of radius $R$ is computed as a function of $R$. The average squared winding number is found to vary linearly with the perimeter of the circle at all temperatures above and below $T_{KT}$, and the slope with $R$ displays a sharp peak near the specific heat peak, decreasing then to a value at infinite temperature that is in agreement with an early theory by Dhar. We have also computed the vortex-vortex distribution functions, finding an asymptotic power-law variation in the vortex separation distance at all temperatures. In conjunction with a Coulomb-gas sum rule on the perimeter fluctuations, these can be used to successfully model the start of the perimeter-slope peak in the region below $T_{KT}$.

Widely applicable, modified Green-Kubo expressions for the local diffusion coefficient ($D_l$) are obtained using linear response theory. In contrast to past definitions in use, these expressions are statistical mechanical results. Molecular simulations of systems with anisotropic diffusion and an inhomogeneous density profile confirm the validity of the results. Diffusion coefficients determined from different expressions in terms of currents and velocity correlations agree in the limit of large systems. Furthermore, they apply to arbitrarily small local regions, making them readily applicable to nanoscale and inhomogeneous systems where knowledge of $D_l$ is important.

To study excitonic effects on high-harmonic generation (HHG) in Mott insulators, we investigate pumped nonequilibrium dynamics in the one-dimensional extended Hubbard model. By employing time-dependent calculations based on the exact diagonalization and infinite time-evolving block decimation methods, we find the strong enhancement of the HHG intensity around the exciton energy. The subcycle analysis in the sub-Mott-gap regime shows that the intensity region of the time-resolved spectrum around the exciton energy splits into two levels and oscillates following the driving electric field. This excitonic dynamics is qualitatively different from the dynamics of free doublon and holon but favorably contributes to HHG in the Mott insulator.

Recent advances in experimental techniques have made it possible to manipulate and measure the magnetization dynamics on the femtosecond time scale which is the same order as the correlation time of the bath degrees of freedom. In the equations of motion of magnetization, the correlation of the bath is represented by the non-Markovian damping. For development of the science and technologies based on the ultrafast magnetization dynamics it is important to understand how the magnetization dynamics depend on the correlation time. It is also important to determine the correlation time experimentally. Here we study the precession dynamics of a small magnet with the non-Markovian damping. Extending the theoretical analysis of Miyazaki and Seki [J. Chem. Phys. 108, 7052 (1998)] we obtain analytical expressions of the precession angular velocity and the effective damping constant for any values of the correlation time under assumption of small Gilbert damping constant. We also propose a possible experiment for determination of the correlation time.

We report bulk magnetization measurements and spatially resolved measurements of magnetic domains in Co3SnS2 single crystals. The results indicate that a previously reported magnetic anomaly at 130K is due to domain wall pinning. Our measurements also reveal a hysteresis between field-cooled-cooling (FCC) and field-cooled-warming (FCW) magnetization curves acquired under a constant magnetic field below 300Oe. The observation rules out the possibility that the anomaly stems from a second-order AFM-FM phase transition. Our results further suggest that changes in the shape of hysteresis loops from 5K to 170K is caused by an unusual temperature-dependent domain nucleation field that changes the sign at around 130K. The Kerr rotation images of the magnetic domains obtained between 120K and 140K support the notion that a domain wall pinning effect exists near 130K.

We study the angular-time evolution that is a parameter-time evolution defined by the entanglement Hamiltonian for the bipartitioned ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain with the open boundary. In particular, we analytically calculate angular-time spin correlation functions $\langle S_n^\alpha(\tau)S_n^\alpha(0)\rangle$ with $\alpha = x,y,z$, using the matrix-product-state (MPS) representation of the valence-bond-solid state with edges. We also investigate how the angular-time evolution operator can be represented in the physical spin space with the use of gauge transformation for the MPS. We then discuss the physical interpretation of the angular-time evolution in the AKLT chain.

Magnetic skyrmions are topologically protected spin swirling vertices, which are promising in device applications due to their particle-like nature and excellent controlability. Magnetic skyrmions have been extensively studied in a variaty of materials, and were proposed to exist in the extreme two-dimensional limit, i.e., in twisted bilayer CrI$_3$ (TBCI). Unfortunately, the magnetic states of TBCIs with small twist angles are disorderly distributed ferromagnetic (FM) and antiferromagnetic (AFM) domains in previous experiments, and thus the method to get rid of disorders in TBCIs is highly desirable. Here we propose the functions of interlayer exchange interactions obtained using first-principles calculations and stored in symmetry-adapted artificial neural networks. Based on them, the subsequent Landau-Lifshitz-Gillbert equation calculations explain the disorderly distributed FM-AFM domains in TBCIs with small twist angles and predict the orderly distributed skyrmions in TBCIs with large twist angles, which can be used in both spintronics and fundamental research.

Periodically-driven open quantum systems that never thermalize exhibit a discrete time-crystal behavior, a non-equilibrium quantum phenomenon that has shown promise in quantum information processing applications. Measurements of time-crystallinity are currently limited to (magneto-) optical experiments in atom-cavity systems and spin-systems making it an indirect measurement. We theoretically show that time-crystallinity can be measured directly in the charge-current from a spin-less Hubbard ladder, which can be simulated on a quantum-dot array. We demonstrate that one can dynamically tune the system out and then back into the time-crystal phase, proving its robustness against external forcings. These findings motivate further theoretical and experimental efforts to simulate the time-crystal phenomena in current-carrying nano-scale systems.

We formulate the Migdal-Eliashberg theory of electron-phonon interactions in terms of classical spins by mapping the free energy to a Heisenberg spin chain in a Zeeman magnetic field. Spin components are energy-integrated normal and anomalous Green's functions and sites of the chain are fermionic Matsubara frequencies. The Zeeman field grows linearly with the spin coordinate and competes with ferromagnetic spin-spin interaction that falls off as the square of the inverse distance. The spin chain representation makes a range of previously unknown properties plain to see. In particular, infinitely many new solutions of the Eliashberg equations both in the normal and superconducting states emerge at strong coupling. These saddle points of the free energy functional correspond to spin flips. We argue that they are also fixed points of kinetic equations and play an essential role in far from equilibrium dynamics of strongly coupled superconductors. Up to an overall phase, the frequency-dependent gap function that minimizes the free energy must be nonnegative. There are strong parallels between our Eliashberg spins and Anderson pseudospins, though the two sets of spins never coincide.

We describe how improvements in methodology and instrumentation for meV-resolved inelastic x-ray scattering (IXS), coupled with a fresh examination of older theory, allow identification of interaction between the quasi-elastic and acoustic dynamical modes in liquid water. This helps explain a decades old controversy about the appearance of additional modes in water spectra, and provides a strong base from which to discuss new phenomena in liquids on the mesoscale.

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intra-chain interactions and the weak interchain coupling. When the intra-chain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally non-exponential, even for spatially uniform perturbations.

We report the effect of high pressure on the superconducting, vortex pinning, and structural properties of a polycrystalline non-centrosymmetric superconductor Re6Hf. The superconducting transition temperature, Tc, reveals a modest decrease as pressure P increases with a slope -0.046 K/GPa (-0.065 K/GPa) estimated from resistivity measurements up to 8 GPa (magnetization measurement ~ 1.1 GPa). Structural analysis up to ~18 GPa reveals monotonic decreases of lattice constant without undergoing any structural transition and a high value of bulk modulus B0= 333.63 GPa, indicating the stability of the structure. Furthermore, the upper critical field and lower critical field at absolute temperature (Hc2(0) & Hc1(0)) decreases slightly from the ambient pressure value as pressure increases up to 2.5 GPa. In addition, up to P ~ 2.5 GPa using thermally activated flux flow of vortices revealed a double linearity field dependence of activation energy of vortices, confirming the coexistence of single and collective pinning vortex states. Moreover, analysis of critical current density using the collective pinning theory showed the transformation of {\delta}Tc to {\delta}l pinning as pressure increases, possibly due to migration of grain boundaries. Besides, the band structure calculations using density functional theory show that density of states decreases modestly with pressure, which may be a possible reason for such a small decrease in Tc by pressure.

By classical and path-integral molecular dynamics simulations, we study the pressure-temperature ($P$-$T$) phase diagram of LaH$_{10}$ to clarify the impact of temperature and atomic zero-point motions. We calculate the XRD pattern and analyze the space group of the crystal structures. For 125 GPa $\leq P\leq$ 150 GPa and $T=300$ K, we show that a highly symmetric $Fm\bar{3}m$ structure, for which superconductivity is particularly favored, is stabilized only by the temperature effect. On the other hand, for $T=200$ K, the interplay between the temperature and quantum effects is crucial to realize the $Fm\bar{3}m$ structure. For $P=$100 GPa and $T=$300 K, we find that the system is close to the critical point of the structural phase transition between the $Fm\bar{3}m$ structure and those with lower symmetries.

Highly transparent superconducting contacts to a topological insulator (TI) remain a persistent challenge on the route to engineer topological superconductivity. Recently, the higher-order TI WTe$_2$ was shown to turn superconducting when placed on palladium (Pd) bottom contacts, demonstrating a promising material system in perusing this goal. Here, we report the diffusion of Pd into WTe$_2$ and the formation of superconducting PdTe$_x$ as the origin of observed superconductivity. We find an atomically sharp interface between the diffusion layer and its host crystal, forming state-of-the-art superconducting contacts to a TI. The diffusion is discovered to be non-uniform along the width of the WTe$_2$ crystal, with a greater extend along the edges compared to the bulk. The potential of this contacting method is highlighted in transport measurements on Josephson junctions by employing external superconducting leads.

The estimation of (n-1)2 interdiffusion coefficients in an n component system requires (n-1) diffusion paths to intersect or pass closely in the (n-1) dimensional space according to the body diagonal diffusion couple method. These interdiffusion coefficients are related to n(n-1) intrinsic (or n tracer diffusion coefficients), which cannot be estimated easily following the Kirkendall marker experiment in a multicomponent system despite their importance for understanding the atomic mechanism of diffusion and the physico-mechanical properties of materials. In this study, the estimation of tracer diffusion coefficients from only two diffusion profiles following the concept of the body diagonal diffusion couple method in a multicomponent system is demonstrated. Subsequently, one can estimate the intrinsic and interdiffusion coefficients. This reduces the overall effort up to a great extent since it needs only two instead of (n-1) diffusion profiles irrespective of the number of components, with an additional benefit of enabling the estimation of all types of diffusion coefficients. The available tracer diffusion coefficients estimated following the radiotracer method are compared to the data estimated in this study following this method. This method can also be extended to the systems in which the radiotracer method is not feasible.

We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the model admits both localized and delocalized phases depending on the strength of the incommensurate potential $V_0$. We show that the particle current contains only odd harmonics in the delocalized phase in contrast to the localised phase where both even and odd harmonics are identified. The relative magnitudes of these even and odd harmonics and sharpness of the peaks can be tuned by varying frequency and the number of cycles of the applied pulse, respectively. In the presence of repulsive interactions, the amplitudes of the even and odd harmonics further depend on the relative strengths of the interaction $U$ and the potential $V_0$. We illustrate that the disorder and interaction-induced phases can be distinguished and characterized through the particle current. Finally, we discuss the dynamics of field induced excitation responsible for exhibiting higher harmonics in the current spectrum.

Epitaxially strained SrRuO3 films have been a model system for understanding the magnetic anisotropy in metallic oxides. In this paper, we investigate the anisotropy of the Ru 4d and O 2p electronic structure and magnetic properties using high-quality epitaxially strained (compressive and tensile) SrRuO3 films grown by machine-learning-assisted molecular beam epitaxy. The element-specific magnetic properties and the hybridization between the Ru 4d and O 2p orbitals were characterized by Ru M2,3-edge and O K-edge soft X-ray absorption spectroscopy and X-ray magnetic circular dichroism measurements. The magnetization curves for the Ru 4d and O 2p magnetic moments are identical, irrespective of the strain type, indicating the strong magnetic coupling between the Ru and O ions. The electronic structure and the orbital magnetic moment relative to the spin magnetic moment are isotropic despite the perpendicular and in-plane magnetic anisotropy in the compressive-strained and tensile-strained SrRuO3 films; i.e., the orbital magnetic moments have a negligibly small contribution to the magnetic anisotropy. This result contradicts Bruno model, where magnetic anisotropy arises from the difference in the orbital magnetic moment between the perpendicular and in-plane directions. Contributions of strain-induced electric quadrupole moments to the magnetic anisotropy are discussed, too.

Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between the diffusing particle and the target. While an exact solution of this problem was recently derived in the form of a spectral expansion over the eigenbasis of the Dirichlet-to-Neumann operator, the latter is generally difficult to access for an arbitrary target. In this paper, we present three complementary approaches to obtain explicit approximations for the probability density of the rescaled number of encounters with a small target in a bounded confining domain. In particular, we derive a simple fully explicit approximation, which depends only on a few geometric characteristics such as the surface area and the harmonic capacity of the target, and the volume of the confining domain. We discuss the advantages and limitations of three approaches and check their accuracy. We also deduce an explicit approximation for the distribution of the first-crossing time, at which the number of encounters exceeds a prescribed threshold. Its relations to common first-passage time problems are discussed.

We study the interaction-induced migration of bubbles in shear flow and observe that bubbles suspended in elastoviscoplastic emulsions organise into chains aligned in the flow direction, similarly to particles in viscoelastic fluids. To investigate the driving mechanism, we perform experiments and simulations on bubble pairs, using suspending fluids with different rheological properties. First, we notice that, for all fluids, the interaction type depends on the relative position of the bubbles. If they are aligned in the vorticity direction, they repel, if not, they attract each other. The simulations show a similar behavior in Newtonian fluids as in viscoelastic and elastoviscoplastic fluids, as long as the capillary number is sufficiently large. This shows that the interaction-related migration of the bubbles is strongly affected by the bubble deformation.

In this paper, we revisit the high-pressure behavior of BaZrO3 by a combination of first-principle calculations, Raman spectroscopy, and x-ray diffraction under high pressure. We confirm experimentally the cubic-to-tetragonal transition at 10 GPa and find no evidence for any other phase transition up to 45 GPa, the highest pressures investigated, at variance with past reports. We re-investigate phase stability with density functional theory considering not only the known tetragonal (I4/mcm) phase but also other potential antiferrodistortive candidates. This shows that the tetragonal phase becomes progressively more stable upon increasing pressure as compared to phases with more complex tilt systems. The possibility for a second transition to another tilted phase at higher pressures, and in particular to the very common orthorhombic Pnma structure, is therefore ruled out.

A supersolid, a counter-intuitive quantum state in which a rigid lattice of particles flows without resistance, has to date not been unambiguously realised. Here we reveal a supersolid ground state of excitons in a double-layer semiconductor heterostructure over a wide range of layer separations outside the focus of recent experiments. This supersolid conforms to the original Chester supersolid with one exciton per supersolid site, as distinct from the alternative version reported in cold-atom systems of a periodic modulation of the superfluid density. We provide the phase diagram augmented by the supersolid. This new phase appears at layer separations much smaller than the predicted exciton normal solid, and it persists up to a solid--solid transition where the quantum phase coherence collapses. The ranges of layer separations and exciton densities in our phase diagram are well within reach of the current experimental capabilities.

Advanced thermostats for molecular dynamics are proposed on the base of the rigorous Langevin dynamics. Because the latter accounts properly for the subsystem-bath interactions, the bath anisotropy and nonuniformity are described by the relevant friction tensor. The developed model reflects appropriately the relativistic dynamics of the subsystem evolution with large momenta of the subsystem particles as well as the nonlinear friction at high temperature.

PtBi2 is a Weyl semimetal, which demonstrates superconductivity with low critical temperature Tc ~ 0.6 K in the bulk. Here, we report our study of electron-phonon interaction (EPI) in trigonal PtBi2 by the Yanson point contact (PC) spectroscopy and presenting the observation of PC enhanced superconductivity. We show, that the Yansons PC spectra display a broad maximum around 15 meV, indicating, apparently, EPI mechanism of Cooper pairing in PtBi2. Moreover, we discovered a substantial increase of Tc up to ~ 3.5 K in PCs. The observed Tc is sufficiently higher than the bulk value, as well as detected at hydrostatic pressure. We calculated the phonon density of states and Eliashberg EPI function in PtBi2 within the framework of the density functional theory. A comparison of experimental data with theoretical calculations showed acceptable agreement. The theoretical Tc is 3.5 K, which corresponds to the experimental value.

We investigate high-order harmonic generations (HHGs) under the comparison of Weyl cones in two types. Due to the hyperboloidal electron pocket structure, strong noncentrosymmetrical generations in high orders are observed around a single type-II Weyl point, especially at frequency zero. Such remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition. Under weak pulse electric field , the linear optical response of a non-tilted Weyl cone is consistent with the Kubo theory. With more numerical simulations, we conclude the non-zero chemical potential can enhance the even-order generations, from the slightly tilted system to the over-tilted systems. In consideration of dynamical symmetries, type-I and -II Weyl cones also show different selective responses under the circularly polarized light. Finally, using a more realistic model containing two pairs of Weyl points, we demonstrate the paired Weyl points with opposite chirality could suppress the overall even-order generations.

A central topic in current research in non-equilibrium physics is the design of pathways to control and induce order in correlated electron materials with time-dependent electromagnetic fields. The theoretical description of such processes, in particular in two spatial dimensions, is very challenging and often relies on phenomenological modelling in terms of free energy landscapes. Here, we present a semiclassical scheme that describes dephasing dynamics beyond mean-field and allows to simulate the light-induced manipulation of prethermal order in a two-dimensional model with competing phases microscopically. We calculate the time-evolution of the relevant order parameters under pulsed driving. We find that the induced prethermal order does not depend on the amount of absorbed energy alone but also explicitly on the driving frequency and amplitude. While this dependency is pronounced in the low-frequency regime, it is suppressed at high driving frequencies.

Electron-hole pairs in organic photovoltaics dissociate efficiently despite their Coulomb-binding energy exceeding thermal energy at room temperature. The electronic states involved in charge separation couple to structured vibrational environments containing multiple underdamped modes. The non-perturbative simulations of such large, spatially extended electronic-vibrational (vibronic) systems remains an outstanding challenge. Current methods bypass this difficulty by considering effective one-dimensional Coulomb potentials or unstructured environments. Here we extend and apply a recently developed method for the non-perturbative simulation of open quantum systems to the dynamics of charge separation in one, two and three-dimensional donor-acceptor networks. This allows us to identify the precise conditions in which underdamped vibrational motion induces efficient long-range charge separation. Our analysis provides a comprehensive picture of ultrafast charge separation by showing how different mechanisms driven either by electronic or vibronic couplings are well differentiated for a wide range of driving forces and how entropic effects become apparent in large vibronic systems. These results allow us to quantify the relative importance of electronic and vibronic contributions in organic photovoltaics and provide a toolbox for the design of efficient charge separation pathways in artificial nanostructures.

Quasi-two-dimensional layered BiSe, a natural super-lattice with Bi2Se3-Bi2-Bi2Se3 units, has recently been predicted to be a dual topological insulator, simultaneously weak topological insulator as well as topological crystalline insulator. Here using structural, transport, spectroscopic measurements and density functional theory calculations, we show that BiSe exhibits rich phase diagram with the emergence of superconductivity with Tc ~8K under pressure. Sequential structural transitions into SnSe-type energetically tangled orthorhombic and CsCl-type cubic structures having distinct superconducting properties are identified at 8 GPa and 13 GPa respectively. Our observation of weak-antilocalization in magneto-conductivity suggests that spin-orbit coupling (SOC) plays a significant role in retaining non-trivial band topology in the trigonal phase with possible realization of 2D topological superconductivity. Theoretical analysis reveals that SOC significantly enhances superconducting Tc of the high-pressure cubic phase through an increase in electron-phonon coupling strength. Simultaneous emergence of Dirac-like surface states suggests cubic BiSe as a suitable candidate for the 3D-topological superconductor.

We investigate shock-compressed copper in the warm dense matter regime by means of density functional theory molecular dynamics simulations. We use neural-network-driven interatomic potentials to increase the size of the simulation box and extract thermodynamic properties in the hydrodynamic limit. We show the agreement of our simulation results with experimental data for solid copper at ambient conditions and liquid copper near the melting point under ambient pressure. Furthermore, a thorough analysis of the dynamic ion-ion structure factor in shock-compressed copper is performed and the adiabatic speed of sound is extracted and compared with experimental data.

We develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. Another significant advantage of the flat norm is that it allows the response of the system at one frequency to be inferred from data at nearby frequencies. We demonstrate and verify the approach by means of two test cases, a polymeric truss structure characterized by DMA data and a 3D soft gel sample characterized by MRE data. The examples demonstrate the ease of implementation of the Data-Driven scheme within conventional commercial codes and its robust convergence properties, both with respect to the solver and the data.

We consider a statistical mechanics of rotating ideal gas consisting of classical non-relativistic spinning particles. The microscopic structure elements of the system are massive point particles with a nonzero proper angular momentum. The norm of proper angular momentum is determined by spin. The direction of proper angular momentum changes continuously. Applying the Gibbs canonical formalism for the rotating system, we construct the one-particle distribution function, generalising the usual Maxwell-Boltzmann distribution, and the partition function of the system. The model demonstrates a set of chiral effects caused by interaction of spin and macroscopic rotation, including the change of entropy, heat capacity, chemical potential and angular momentum.

In recent years it has become clear that the transport of excitons and charge carriers in molecular systems can be enhanced by coherent coupling with photons, giving rise to the formation of hybrid excitations known as polaritons. Such enhancement has far-reaching technological implications, however, the enhancement mechanism and the transport nature of these composite light-matter excitations in such systems still remain elusive. Here we map the ultrafast spatiotemporal dynamics of surface-bound optical waves strongly coupled to a self-assembled molecular layer and fully resolve them in energy/momentum space. Our studies reveal intricate behavior which stems from the hybrid nature of polaritons. We find that the balance between the molecular disorder and long-range correlations induced by the coherent mixing between light and matter leads to a mobility transition between diffusive and ballistic transport, which can be controlled by varying the light-matter composition of the polaritons. Furthermore, we directly demonstrate that the coupling with light can enhance the diffusion coefficient of molecular excitons by six orders of magnitude and even lead to ballistic flow at two-thirds the speed of light.

Since the discovery of topological insulators a lot of research effort has been devoted to magnetic topological materials, in which non-trivial spin properties can be controlled by magnetic fields, culminating in a wealth of fundamental phenomena and possible applications. The main focus was on ferromagnetic materials that can host Weyl fermions and therefore spin textured Fermi arcs. The recent discovery of Fermi arcs and new magnetic bands splitting in antiferromagnet (AFM) NdBi has opened up new avenues for exploration. Here we show that these uncharted effects are not restricted to this specific compound, but rather emerge in CeBi, NdBi, and NdSb when they undergo paramagnetic to AFM transition. Our data show that the Fermi arcs in NdSb have 2-fold symmetry, leading to strong anisotropy that may enhance effects of spin textures on transport properties. Our findings thus demonstrate that the RBi and RSb series are materials that host magnetic Fermi arcs and may be a potential platform for modern spintronics.

We have witnessed a wide range of theoretical as well as experimental investigations to envisage external stimuli induced changes in electronic, optical, and magnetic properties in the metal organic complexes, while hybrid perovskites have recently joined this exciting league of explorations. The flexible organic linkers in such complexes are ideal for triggering not only spin transitions but also a plethora of different responses under the influence of external stimuli like pressure, temperature, and light. A diverse range of applications particularly in the field of optoelectronics, spintronics, and energy scavenging have been manifested. Hysteresis associated with light induced transitions and spin-crossover governed by pressure and temperature are promising phenomena for the design principles behind memory devices and optical switches. Pressure induced optical properties tuning or piezochromism has also emerged as one of the prominent areas in the field of hybrid perovskites. It is thus imperative to have a clear understanding of how the tuning in electronic, optical, and magnetic properties occur under various stimuli. Selectivity of the stimulus could be influential behind the maximum efficiency in the field of energy and optoelectronic research to determine in what future directions this field could be driven from the perspective of futuristic material properties. This review though primarily focuses on the theoretical aspects of understanding the different mechanisms of the phenomena, does provide a unique overview of the experimental literature too, such that relevant device applications can be considered through a future roadmap of tuning paradigm of external stimuli. It also provides an insight as to how energy and memory storage may be combined by using the principles of spin transition in metal organic complexes.

So far, experimentally realized quantum anomalous Hall (QAH) insulators all exhibit ferromagnetic order and the QAH effect only occurs at very low temperatures; Conceptually, the QAH effect is based on ferromagnetism or staggered flux. On the other hand, up to now the QAH effect in antiferromagnetic (AFM) systems has never been reported. In this letter, we realize the QAH effect by proposing a four-band lattice model with static AFM order, which indicates the QAH effect can be found in AFM materials with low lattice symmetry. Then, as a prototype, we demonstrate that a monolayer CrO can be switched from an AFM Weyl semimetal to an AFM QAH insulator by applying strain to lower its symmetry, based on theoretical analysis and the first-principles electronic structure calculations. Our work not only proposes a new scenario to search for QAH insulators,but also reveals a way to considerably increase the critical temperature of the QAH phase.

We analyze the micromagnetics of short longitudinal modulations of a high magnetization material in cylindrical nanowires made of a soft-magnetic material of lower magnetization such as Permalloy, combining magnetic microscopy, analytical modeling and micromagnetic simulations. The mismatch of magnetization induces curling of magnetization around the axis in the modulations, in an attempt to screen the interfacial magnetic charges. The curling angle increases with modulation length, until a plateau is reached with nearly full charge screening for a specific length scale~$\Delta_\mathrm{mod}$, larger than the dipolar exchange length of any of the two materials. The curling circulation can be switched by the \OErsted field arising from a charge current with typical magnitude $10^{12} A/m^{2}$, and reaching a maximum for $\Delta_\mathrm{mod}$.

A general method was developed to intercalate metals under layered materials through a controlled density of sputtered defects. The method has been already applied to study a range of metals intercalated under graphite and different types of morphologies were realized. In the current work, we extend the method to the study of intercalation under MoS2 noting that work on this system is rather limited. We use Cu as the prototype metal for comparison with Cu intercalation under graphite. Although the growth conditions needed for intercalation under graphite and MoS2 are similar, the type of intercalated phases is very different. Each Cu island which nucleates on top of MoS2 during Cu deposition provides material that transfers Cu below MoS2 through sputtered defects under the island base; this transfer results in a uniform intercalated Cu "carpet" morphology that extends over the mesoscale. On the contrary, Cu intercalation under graphite results in well separated, compact islands formed by monomer detachment from small Cu islands on top, and transfer below through defects far from the islands. Several structural techniques Secondary Electron Microscopy (SEM), Atomic Force Microscopy (AFM), spectroscopic techniques X-ray Photoelectron Spectroscopy (XPS), and Electron Dispersive Spectroscopy (EDS), are used for the characterization of the intercalated Cu layer.

Probing an isolated Majorana zero mode is predicted to reveal a tunneling conductance quantized at $2e^2/h$ at zero temperature. Experimentally, a zero-bias peak (ZBP) is expected and its height should remain robust against relevant parameter tuning, forming a quantized plateau. Here, we report the observation of large ZBPs in a thin InAs-Al hybrid nanowire device. The ZBP height can stick close to $2e^2/h$, mostly within 5% tolerance, by sweeping gate voltages and magnetic field. We further map out the phase diagram and identify two plateau regions in the phase space. Our result constitutes a step forward towards establishing Majorana zero modes.

PbTe is a semiconductor with promising properties for topological quantum computing applications. Here we characterize quantum dots in PbTe nanowires selectively grown on InP. Charge stability diagrams at zero magnetic field reveal large even-odd spacing between Coulomb blockade peaks, charging energies below 140$~\mathrm{\mu eV}$ and Kondo peaks in odd Coulomb diamonds. We attribute the large even-odd spacing to the large dielectric constant and small effective electron mass of PbTe. By studying the Zeeman-induced level and Kondo splitting in finite magnetic fields, we extract the electron $g$-factor as a function of magnetic field direction. We find the $g$-factor tensor to be highly anisotropic, with principal $g$-factors ranging from 0.9 to 22.4, and to depend on the electronic configuration of the devices. These results indicate strong Rashba spin-orbit interaction in our PbTe quantum dots.

We report experimental evidence of a Gardner-like transition from variable to persistent force contacts in a two-dimensional, bidisperse granular crystal by analyzing the variability of both particle positions and force networks formed under uniaxial compression. Starting from densities just above the freezing transition, and for variable amounts of additional compression, we compare configurations to both their own initial state, and to an ensemble of equivalent, reinitialized states. This protocol shows that force contacts are largely undetermined when the density is below a Gardner-like transition, after which they gradually transition to being persistent, being fully so only above the jamming point. We associate the disorder that underlies this effect to the size of the microscopic asperities of the photoelastic disks used, by analogy to other mechanisms that have been previously predicted theoretically.

We consider an ideal Bose gas enclosed in a $d$-dimensional slab of thickness $D$. Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab's walls. The variance evaluated per unit wall area is shown to decay like $ \Delta_{var}/D$ for large $D$. The amplitude $ \Delta_{var}$ is a non-universal function of two scaling variables $\lambda/ \xi$ and $D/ \xi$, where $\lambda$ is the thermal de Broglie wavelength and $\xi$ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose-Einstein condensate the amplitude $ \Delta_{var}$ retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form $(D/L)^{\frac{d-1}{2}}\, (D/\lambda)^{d/2}$, where $L$ is the linear size of the wall.

Recent experimental observations have demonstrated that topological defects can facilitate the development of sharp features, such as tentacles and protrusions, at the early stage of embryonic morphogenesis. Whereas these observations echo established knowledge about the interplay between geometry and topology in two-dimensional passive liquid crystals, the role of activity has mostly remained unexplored. In this article we focus on deformable shells consisting of either polar or nematic active liquid crystals and demonstrate that activity renders the mechanical coupling between defects and curvature much more involved and versatile than previously thought. Using a combination of linear stability analysis and three-dimensional computational fluid dynamics, we demonstrate that such a coupling can in fact be tuned, depending on the type of liquid crystal order, the specific structure of the defect (i.e. asters or vortices) and the nature of the active forces. In polar systems, this can drive a spectacular transition from spherical to toroidal topology, in the presence of large extensile activity. Our analysis strengthens the idea that defects could serve as topological morphogens and provides a number of predictions that could be tested in in vitro studies, for instance in the context of organoids.

The fidelity of a variational quantum circuit state prepared within stochastic gradient descent depends on, in addition to the circuit architecture, the number $N_s$ of measurements performed to estimate the gradient components. Simulating the variational quantum eigensolver (VQE) approach applied to two-dimensional frustrated quantum magnets, we observe that this dependence has systematic features. First, the algorithm manifests pronouncedly separated regimes on the $N_s$ axis with state fidelity $\mathcal{F}$ vanishing at $N_s < N_s^c$ and rapidly growing at $N_s > N_s^c$. {The point of transition $N_s^c$ is marked by a peak of energy variance, resembling the behaviour of specific heat in second-order phase transitions.} The extrapolation of the system-dependent threshold value $N_s^c$ to the thermodynamic limit suggests the possibility of obtaining sizable state fidelities with an affordable shots budget, even for large-scale spin clusters. Second, above $N_s^c$, the state infidelity $\mathcal{I} = 1 - \mathcal{F}$ satisfies $\mathcal{I} - \mathcal{I}_0 \propto 1/(\Delta^2 N_s)$, with $\mathcal{I}_0$ representing the circuit's inability to express the exact state, $\mathcal{F}$ is the achieved state fidelity, and $\Delta$ represents the system energy gap. This $1 / \Delta^2$ empirical law implies optimization resources increase inversely proportional to the squared gap of the system. We provide a symmetry-enhanced simulation protocol, which, in case of a closing gap, can significantly reduce the frustrated magnets simulation costs in quantum computers.

We present a holographic quantum simulation algorithm to approximately prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a ($d$-1)-dimensional cross-section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix product states (sto-qMPS), and variationally optimizing the quantum circuits that generate the sto-qMPS tensors, and parameters of the probability distribution generating the stochastic mixture. We demonstrate this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin-chains over a wide temperature range using only a single pair of hardware qubits. We then explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits through classical simulations and establish empirical relationships between the circuit resources and the accuracy of the variational free-energy.

Can a micron sized sack of interacting molecules understand, and adapt to a constantly-fluctuating environment? Cellular life provides an existence proof in the affirmative, but the principles that allow for life's existence are far from being proven. One challenge in engineering and understanding biochemical computation is the intrinsic noise due to chemical fluctuations. In this paper, we draw insights from machine learning theory, chemical reaction network theory, and statistical physics to show that the broad and biologically relevant class of detailed balanced chemical reaction networks is capable of representing and conditioning complex distributions. These results illustrate how a biochemical computer can use intrinsic chemical noise to perform complex computations. Furthermore, we use our explicit physical model to derive thermodynamic costs of inference.

We introduce a computational Maxwell-Bloch framework for investigating out of equilibrium optical emitters in open cavity-less systems. To do so, we compute the pulse-induced dynamics of each emitter from fundamental light-matter interactions and self-consistently calculate their radiative coupling, including phase inhomogeneity from propagation effects. This semiclassical framework is applied to open systems of quantum dots with different density and dipolar coupling. We observe that signatures of superradiant behavior, such as directionality and faster decay, are weak for systems with extensions comparable to $\lambda/2$. In contrast, subradiant features are robust and can produce long-term population trapping effects. This computational tool enables quantitative investigations of large optical ensembles in the time domain and could be used to design new systems with enhanced superradiant and subradiant properties.

The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by microscopic machines. We provide the fundamental bound on the amount of ergotropy which can be extracted from environment in this way. The bound is expressed in terms of the non-equilibrium free energy difference and can be saturated in the limit of infinite dimension of the system's Hamiltonian. The ergotropy extraction process leading to this saturation is numerically analyzed for finite dimensional systems. Furthermore, we apply the idea of extraction of ergotropy from environment in a design of a new class of stroke heat engines, which we label open-cycle engines. Efficiency and work production of these machines can be completely optimized for systems of dimensions 2 and 3, and numerical analysis is provided for higher dimensions.

The advance of topological photonics has heralded a revolution for manipulating light as well as for the development of novel photonic devices such as topological insulator lasers. Here, we demonstrate topological lasing of circular polarization in a polymer-cholesteric liquid crystal (P-CLC) superlattice, tunable in the visible wavelength regime. By use of the femtosecond-laser direct-writing and self-assembling techniques, we establish the P-CLC superlattice with a controlled mini-band structure and a topological interface defect, thereby achieving a low threshold for robust topological lasing at about 0.4 uJ. Thanks to the chiral liquid crystal, not only the emission wavelength is thermally tuned, but the circularly polarized lasing is readily achieved. Our results bring about the possibility to realize compact and integrated topological photonic devices at low cost, as well as to engineer an ideal platform for exploring topological physics that involves light-matter interaction in soft-matter environments.

We demonstrate a spectrum demodulation technique for greatly speeding up the data acquisition rate in scanning nitrogen-vacancy center magnetometry. Our method relies on a periodic excitation of the electron spin resonance by fast, wide-band frequency sweeps combined with a phase-locked detection of the photo-luminescence signal. The method can be extended by a frequency feedback to realize real-time tracking of the spin resonance. Fast scanning magnetometry is especially useful for samples where the signal dynamic range is large, of order millitesla, like for ferro- or ferrimagnets. We demonstrate our method by mapping stray fields above the model antiferromagnet $\alpha$-Fe$_2$O$_3$ (hematite) at pixel rates of up to 100\,Hz and an image resolution exceeding one megapixel.

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

We propose that a minimal bond cut surface is characterized by entanglement distillation in tensor networks. Our proposal is not only consistent with the holographic models of perfect or tree tensor networks, but also can be applied for several different classes of tensor networks including matrix product states and multi-scale entanglement renormalization ansatz. We confirmed our proposal by a numerical simulation based on the random tensor network. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography.

The rapid progress of machine learning interatomic potentials over the past couple of years produced a number of new architectures. Particularly notable among these are the Atomic Cluster Expansion (ACE), which unified many of the earlier ideas around atom density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message passing neural network with equivariant features that showed state of the art accuracy. In this work, we construct a mathematical framework that unifies these models: ACE is generalised so that it can be recast as one layer of a multi-layer architecture. From another point of view, the linearised version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in the unified design space. We demonstrate this by an ablation study of NequIP via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, and shed some light on which design choices are critical for achieving high accuracy. Finally, we present BOTNet (Body-Ordered-Tensor-Network), a much-simplified version of NequIP, which has an interpretable architecture and maintains accuracy on benchmark datasets.

Here, steady-state reaction networks are inspected from the viewpoint of individual tagged molecules jumping among their chemical states upon the occurrence of reactive events. Such an agent-based viewpoint is useful for selectively characterizing the behavior of functional molecules, especially in the presence of bimolecular processes. We present the tools for simulating the jump dynamics both in the macroscopic limit and in the small-volume sample where the numbers of reactive molecules are of the order of few units with an inherently stochastic kinetics. The focus is on how an ideal spatial "compartmentalization" may affect the dynamical features of the tagged molecule. Our general approach is applied to a synthetic light-driven supramolecular pump composed of ring-like and axle-like molecules that dynamically assemble and disassemble, originating an average ring-through-axle directed motion under constant irradiation. In such an example, the dynamical feature of interest is the completion time of direct/inverse cycles of tagged rings and axles. We find a surprisingly strong robustness of the average cycle times with respect to the system's size. This is explained in the presence of rate-determining unimolecular processes, which may, therefore, play a crucial role in stabilizing the behavior of small chemical systems against strong fluctuations in the number of molecules.

Quantum machine learning represents a promising avenue for data processing, also for purposes of sequential temporal data analysis, as recently proposed in quantum reservoir computing (QRC). The possibility to operate on several platforms and noise intermediate-scale quantum devices makes QRC a timely topic. A challenge that has not been addressed yet, however, is how to efficiently include quantum measurement in realistic protocols, while retaining the reservoir memory needed for sequential time series processing and preserving the quantum advantage offered by large Hilbert spaces. In this work, we propose different measurement protocols and assess their efficiency in terms of resources, through theoretical predictions and numerical analysis. We show that it is possible to exploit the quantumness of the reservoir and to obtain ideal performance both for memory and forecasting tasks with two successful measurement protocols. One consists in rewinding part of the dynamics determined by the fading memory of the reservoir and storing the corresponding data of the input sequence, while the other employs weak measurements operating online at the trade-off where information can be extracted accurately and without hindering the needed memory. Our work establishes the conditions for efficient protocols, being the fading memory time a key factor, and demonstrates the possibility of performing genuine online time-series processing with quantum systems.