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The definition of heat in quantum mechanics is ambiguous. Complications arise in particular when the coupling between a quantum system and an environment is non-negligible, as the boundary between the two becomes blurred, making the distinction between system and environment difficult to draw. The reaction coordinate mapping can be used in such regimes to redraw the boundary between the system and environment. Here we combine the reaction coordinate technique with a two-point measurement protocol to compare two different definitions of heat: energetic changes in the full environment Hamiltonian (prior to the mapping), and energetic changes in the residual environment Hamiltonian (after the mapping). We find that the latter definition displays behaviour more expected of a thermal environment in the highly non-Markovian regime considered., Comment: 12 pages, 5 figures. Comments welcome!

We study the sine-Gordon quantum field theory at finite temperature by generalizing the method of random surfaces to compute the free energy and one-point functions of exponential operators non-perturbatively. Focusing on the gapped phase of the sine-Gordon model, we demonstrate the method's accuracy by comparing our results to the predictions of other methods and to exact results in the thermodynamic limit. We find excellent agreement between the method of random surfaces and other approaches when the temperature is not too small with respect to the mass gap. Extending the method to more general problems in strongly interacting one-dimensional quantum systems is discussed., Comment: 11+5 pages, 3+5 figures

Along recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy $S_{BH}\propto A/l_P^2$ ($A \equiv$ area; $l_P \equiv$ Planck length) systematically plays a crucial theoretical role although it has a serious drawback, namely that it violates the thermodynamic extensivity of spatially-three-dimensional systems. Still, its intriguing area dependence points out the relevance of considering the form $W(N)\sim \mu^{N^\gamma}\;\;(\mu >1;\gamma >0)$, $W$ and $N$ respectively being the total number of microscopic possibilities and the number of components; $\gamma=1$ corresponds to standard Boltzmann-Gibbs (BG) statistical mechanics. For this $W(N)$ asymptotic behavior, we introduce here, on a group-theory basis, the entropic functional $S_{\alpha,\gamma}=k \Bigl[ \frac{\ln \Sigma_{i=1}^W p_i^\alpha}{1-\alpha} \Bigr]^{\frac{1}{\gamma}} \;(\alpha \in \mathbb{R};\,S_{1,1}=S_{BG}\equiv-k\sum_{i=1}^W p_i \ln p_i)$. This functional simultaneously is {\it extensive} (as required by thermodynamics) and {\it composable} (as required for logic consistency), $\forall (\alpha,\gamma)$. We further show that $(\alpha,\gamma)=(1,2/3)$ satisfactorily agrees with cosmological data measuring neutrinos, Big Bang nucleosynthesis and the relic abundance of cold dark matter particles, as well as dynamical and geometrical cosmological data sets., Comment: 5 pages, 2 figures

We present results from the molecular dynamics (MD) simulation of surface-directed spinodal decomposition (SDSD) in binary fluid mixtures ($A+B$) with off-critical compositions. The aim is to elucidate the role of composition ratio in the early-time wetting kinetics under the influence of long-range surface potential. In our simulations, the attractive part of surface potential varies as $V(z)= -\epsilon_a/z^{n}$, with $\epsilon_{a}$ being the surface-potential strength. The surface prefers `$A$' species to form the wetting layer. Its thickness [$R_1(t)$] for the majority wetting (number of $A$-type particles [$N_A$] > number of $B$-type particles [$N_B$]), grows as a power-law with an exponent $1/(n+2)$. This is consistent with the early-time kinetics in the form of potential-dependent growth present in the Puri-Binder model. However, for minority wetting ($N_A$ < $N_B$), the growth exponent in $R_1(t)$ is less than $1/(n+2)$. Furthermore, on decreasing the field strength $\epsilon_{a}$, we recover $1/(n+2)$ for a minority wetting case. We provide phenomenological arguments to explain the early-time wetting kinetics for both cases., Comment: 11 pages, 7 figures

We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated application of these channels can be seen as a simple model for the thermalization process of a many-body system. We study its steady state perturbatively by interpolating between the 1-local and 2-local channels with a perturbation parameter $\epsilon$. We prove that under very general conditions, these states are Gibbs states of a quasi-local Hamiltonian. Expanding this Hamiltonian as a series in $\epsilon$, we show that the $k$'th order term corresponds to a $(k+1)$-local interaction term in the Hamiltonian, which follows the same interaction graph as the Kraus channel. We also prove a complementary result suggesting the existence of an interaction strength threshold, under which the total weight of the high-order terms in the Hamiltonian decays exponentially fast. This result also implies a quasi-polynomial classical algorithm for computing the expectation value of local observables in such steady states. Finally, we also present numerical simulations of various channels that support our theoretical claims., Comment: 26 pages

Equilibrium thermodynamics is grounded in the law of energy conservation, with a specific focus on how systems exchange energy with their environment during transitions between equilibrium states. These transitions are typically characterized by quantities such as heat absorption and the work needed to alter the system's volume. This study is inspired by the potential to develop an analogous, straightforward thermodynamic description for systems that are out of equilibrium. Here, we explore the global energy exchanges that occur during transitions between these nonequilibrium states. We study a system with heat flow and an external (gravity) field that exhibits macroscopic motion, such as Rayleigh-B\'enard convection. We show that the formula for system's energy exchange has the same form as in equilibrium. It opens the possibility of describing out-of-equilibrium systems using a few simple laws similar to equilibrium thermodynamics., Comment: 6 pages, 1 figure

The Achlioptas process, which suppresses the aggregation of large-sized clusters, can exhibit an explosive percolation (EP) where the order parameter emerges abruptly yet continuously in the thermodynamic limit. It is known that EP is accompanied by an abnormally small critical exponent of the order parameter. In this paper, we report that a novel type of EP occurs on a Bethe lattice, where the critical exponent of the order parameter is the same as in ordinary bond percolation based on numerical analysis. This is likely due to the property of a finite Bethe lattice that the number of sites on the surface with only one neighbor is extensive to the system size. To overcome this finite size effect, we consider an approximate size of the cluster that each site on the surface along its branch belongs to, and accordingly approximate the sizes of an extensive number of clusters during simulation. As a result, the Achlioptas process becomes ineffective and the order parameter behaves like that of ordinary percolation at the threshold. We support this result by measuring other critical exponents as well., Comment: 6 pages, 5 figures

When a link is occupied to restrict the growth of large clusters using the size information of a finite number of finite clusters, so-called local information, an abrupt but continuous transition is exhibited. We report here that a hybrid transition can occur if each node rewires its links to restrict the growth of large clusters using local information continuously up to a finite number of rewirings. For example, on a branch of a Bethe lattice with coordination number $4$, each node rewires its outgoing links to its descendants several times in ascending order of cluster size to reach a steady state. Then a hybrid transition with nontrivial critical exponents occurs as a function of the link fraction at the steady state. We observe this phenomenon even on a Bethe lattice without hierarchy, supporting that such a phenomenon may occur on diverse tree networks with finite degrees., Comment: 10 pages, 8 figures

Viscosity is the resistance of a liquid to flow, governed by atomic-scale friction between its constituent atoms. While viscosity can be directly computed using the Green-Kubo formalism, this method does not fully elucidate the physical mechanisms underlying such momentum transport coefficient. In fact, the microscopic origin of liquid viscosity remains poorly understood. In this work, we calculate the viscosity of a $\mathrm{Cu_{50}Zr_{50}}$ metallic liquid and a Kob-Andersen model in a large range of temperatures and compare the results with a theoretical formula based on nonaffine linear response and instantaneous normal mode theory. This analysis reveals that only unstable localized instantaneous normal modes (ULINMs) contribute to viscosity, providing a microscopic definition of viscosity as diffusive momentum transport facilitated by local structural excitations mediated by ULINMs as precursors. Leveraging on the concept of configurational entropy, a quantitative model to connect viscosity with ULINMs is also proposed and validated in both the Arrhenius and non-Arrhenius regimes. In summary, our work provides a microscopic definition of liquid viscosity and highlights the fundamental role of ULINMs as its building blocks, ultimately opening the path to an atomic-scale prediction of viscosity in liquids and glasses., Comment: v1: comments welcome!

We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes $g(t) \equiv \langle (\Delta x(t))^{2} \rangle$ for all times at which $g(t)$ was measured, and that gives values for the logarithmic derivative of $g(t)$ for the same times. By these means we can readily distinguish between regimes in which $g(t)$ follows a power law in time, does not follow a power law in time, or has an inflection point. In a power-law regime, the method accurately determines the exponent, without imposing any assumption as to the exponent's value., Comment: 9 pages, 3 figures

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time-dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems., Comment: 6+13 pages, 3 figures

Fluctuations of observables provide unique insights into the nature of physical systems, and their study stands as a cornerstone of both theoretical and experimental science. Generalized fluctuations, or cumulants, provide information beyond the mean and variance of an observable. In this letter, we develop a systematic method to determine the asymptotic behavior of cumulants of local observables as the region becomes large. Our analysis reveals that the expansion is closely tied to the geometric characteristics of the region and its boundary, with coefficients given by convex moments of the connected correlation function: the latter is integrated against intrinsic volumes of convex polytopes built from the coordinates, which can be interpreted as averaged shadows. A particular application of our method shows that, in two dimensions, the leading behavior of odd cumulants of conserved quantities is topological, specifically depending on the Euler characteristic of the region. We illustrate these results with the paradigmatic strongly-interacting system of two-dimensional quantum Hall state at filling fraction $1/2$, by performing Monte-Carlo calculations of the skewness (third cumulant) of particle number in the Laughlin state., Comment: 4+8 pages, 3+3 figures

The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of $SU(N)$, is studied in the limit where $N$ becomes large and scales as the square root of the number of atoms $n$. This model exhibits additional phases, as well as two different temperature scales related by a factor $N\!/\!\ln N$. The paramagnetic phase splits into a "dense" and a "dilute" phase, separated by a third-order transition and leading to a triple critical point in the scale parameter $n/N^2$ and the temperature, while the ferromagnetic phase exhibits additional structure, and a new paramagnetic-ferromagnetic metastable phase appears at the larger temperature scale. These phases can coexist, becoming stable or metastable as temperature varies. A generalized model in which the number of $SU(N)$-equivalent states enters the partition function with a nontrivial weight, relevant, e.g., when there is gauge invariance in the system, is also studied and shown to manifest similar phases, with the dense-dilute phase transition becoming second-order in the fully gauge invariant case., Comment: 41 pages, 9 figures

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D \propto 1/\rho$ at low densities $\rho$. Our numerical approach generalizes the Dissipation-Assisted Operator Evolution (DAOE) algorithm: in the spirit of the BBGKY hierarchy, we effectively approximate non-local operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low temperature transport., Comment: 5 + 9 pages, 3 + 3 figures. Comments welcome!

Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C, 2350061 (2023)], which is directly reflected in the eigenvalues of these matrices. When these evolutions are analyzed in the mean-field regime, an important question arises: Can the Langevin equation, when translated into maps, perform the same function? Some studies suggest that this method may also capture the chaotic behavior of certain systems. In this work, we propose that the spectral properties of random matrices constructed from maps derived from deterministic or stochastic differential equations can indicate the critical or chaotic behavior of such systems. For chaotic systems, we need only the evolution of iterated Hamiltonian equations, and for spin systems, the Langevin maps obtained from mean-field equations suffice, thus avoiding the need for Monte Carlo (MC) simulations or other techniques., Comment: 19 pages, 5 figures

Quasicrystals are materials that exhibit long-range order without translational periodicity. In soft matter, the most commonly observed quasicrystal has 12-fold symmetry and consists of tilings made out of squares and triangles. Intriguingly, both in experiments and simulations, these tilings nearly always appear with many vacancy-related defects that are connected to an additional tile: a rhombus. In this letter, we explore the role of rhombus defects on the entropy of square-triangle 12-fold quasicrystals. We introduce a novel lattice-based Monte Carlo simulation method that uses open boundaries to allow the concentration of defects to fluctuate. Our simulations show that rhombus tiles significantly increase the configurational entropy of the quasicrystal phase, enhancing its stability. These findings highlight the critical role of defects in stabilizing soft-matter quasicrystals., Comment: 6 pages, 4 figures

We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two $XY$ spin chains that are coupled through Ising $ZZ$ interaction. The spin ladder model is then examined within the semiclassical limit using a spin-coherent state basis, where the dynamics is governed by a set of coupled Landau-Lifshitz-Gilbert equations. The non-Hermitian interactions in this model generate a spin-transfer torque term. We analyze the system's evolution toward several potential steady states, including a state of decoupled chains that is accessible when each chain has uniform initial conditions. Other possible steady states involve dimerized configurations with decoupled rungs, where the rung spins are either ferromagnetically or antiferromagnetically coupled, depending on the sign of the imaginary interactions. The spin dynamics is then studied in the infinite-temperature limit, which favors dimerized steady states. Despite the decoupled rungs, we observe the formation of ferromagnetic domains along each chain in the steady state. Additionally, we investigate the spin correlation functions and identify signatures of anomalous spin dynamics., Comment: 12 pages, 9 figures

We introduce bipartite projected ensembles (BPEs) for quantum many-body wave functions, which consist of pure states supported on two local subsystems, with each state associated with the outcome of a projective measurement of the complementary subsystem in a fixed local basis. We demonstrate that the corresponding ensemble-averaged entanglements (EAEs) between two subsystems can effectively identify entanglement phases. In volume-law entangled states, EAE converges to a nonzero value with increasing distance between subsystems. For critical systems, EAE exhibits power-law decay, and it decays exponentially for area-law systems. Thus, entanglement phase transitions can be viewed as a disorder-order phase transition. We also apply BPE and EAE to measured random Clifford circuits to probe measurement-induced phase transitions. We show that EAE serves not only as a witness to phase transitions, but also unveils additional critical phenomena properties, including dynamical scaling and surface critical exponents. Our findings provide an alternative approach to diagnosing entanglement laws, thus enhancing the understanding of entanglement phase transitions. Moreover, given the scalability of measuring EAE in quantum simulators, our results hold promise for impacting quantum simulations., Comment: 6+2 pages, 4+1 figures

New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering or low-dimensional projections. Here we use the principle of maximum entropy to obtain a probabilistic description that captures the observed presence or absence of mRNAs from hundreds of genes in cells from the mammalian brain. We construct the Ising model compatible with experimental means and pairwise correlations, and validate it by showing that it gives good predictions for higher-order statistics. We notice that the probability distribution of cell states has many local maxima. By labeling cell states according to the associated maximum, we obtain a cell classification that agrees well with previous results that use traditional clustering techniques. Our results provide quantitative descriptions of gene expression statistics and interpretable criteria for defining cell classes, supporting the hypothesis that cell classes emerge from the collective interaction of gene expression levels., Comment: 14 pages, 21 figures

In this paper, we investigate the spectral projection of density matrices in quantum field theory. With appropriate regularization, the spectral projectors of density matrices are expected to be well-defined. These projectors can be obtained using the Riesz projection formula, which allows us to compute both the density of eigenvalues and the expectation values of local operators in the projected states. We find that there are universal divergent terms in the expectation value of the stress energy tensor, where the coefficients depend universally on the density of eigenvalues and a function that describes the dependence of eigenvalues on boundary location. Using projection states, we can construct a series of new states in quantum field theories and discuss their general properties, focusing on the holographic aspects. We observe that quantum fluctuations are suppressed in the semiclassical limit. We also demonstrate that the fixed area state, previously constructed using gravitational path integrals, can be constructed by suitably superposition of appromiate amount of projection states. Additionally, we apply spectral projection to non-Hermitian operators, such as transition matrices, to obtain their eigenvalues and densities. Finally, we highlight potential applications of spectral projections, including the construction of new density and transition matrices and the understanding of superpositions of geometric states., Comment: references added

Through an explicit construction, we assign to any infinite temperature autocorrelation function $C(t)$ a set of functions $\alpha^n(t)$. The construction of $\alpha^n(t)$ from $C(t)$ requires the first $2n$ temporal derivatives of $C(t)$ at times $0$ and $t$. Our focus is on $\alpha^n(t)$ that (almost) monotonously decrease, we call these ``arrows of time functions" (AOTFs). For autocorrelation functions of few body observables we numerically observe the following: An AOTF featuring a low $n$ may always be found unless the the system is in or close to a nonchaotic regime with respect to a variation of some system parameter. All $\alpha^n(t)$ put upper bounds to the respective autocorrelation functions, i.e. $\alpha^n(t) \geq C^2(t)$. Thus the implication of the existence of an AOTF is comparable to that of the H-Theorem, as it indicates a directed approach to equilibrium. We furthermore argue that our numerical finding may to some extent be traced back to the operator growth hypothesis. This argument is laid out in the framework of the so-called recursion method., Comment: 11 pages, 11 figures

Active liquid-liquid phase separation (LLPS) in a confining environment is believed to play an important role in cell biology. Recently, it was shown that when active noise at the microscopic level is included in the classical theory of nucleation and growth then this does not cause the breakdown of detailed balance at the \textit{macroscopic} level provided that the droplet radius is the only collective coordinate. Here, we present a simple model for active LLPS in a confining environment, with the droplet location in a confining potential as a second collective coordinate, and find that detailed balance \textit{is} broken at the macroscopic level in an unusual fashion, using the Fluctuation-Dissipation Theorem as a diagnostic.

The nonequilibrium dynamics of quantum many-body systems have attracted growing attention due to various intriguing phenomena absent in equilibrium physics. One famous example is the quantum Mpemba effect, where the subsystem symmetry is restored faster under a symmetric quench from a more asymmetric initial state. The quantum Mpemba effect has been extensively studied in integrable and chaotic systems. In this Letter, we investigate symmetry restoration and quantum Mpemba effect in many-body localized systems with various initial states. We reveal that the symmetry can still be fully restored in many-body localization phases without approaching thermal equilibrium. Furthermore, we demonstrate that the presence of the quantum Mpemba effect is universal for any initial tilted product state, contrasting to the cases in the chaotic systems where the presence of the quantum Mpemba effect relies on the choice of initial states. We also provide a theoretical analysis of symmetry restoration and quantum Mpemba effects with the help of the effective model for many-body localization. This Letter not only sheds light on extending the quantum Mpemba effect to more non-equilibrium settings but also contributes to a deeper understanding of the many-body localization., Comment: 23 pages (including supplemental materials), 11 figures

Hydrodynamic turbulence exhibits nonequilibrium behaviour with $k^{-5/3}$ energy spectrum, and equilibrium behaviour with $k^{d-1}$ energy spectrum and zero viscosity, where $d$ is the space dimension. Using recursive renormalization group {in Craya-Herring basis}, we show that the nonequilibrium solution is valid only for $d < 6$, whereas equilibrium solution with zero viscosity is the only solution for $d>6$. Thus, $d=6$ is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near $d=2.15$. We also compute the energy flux and Kolmogorov's constants for various $d$'s, and observe that our results are in good agreement with past numerical results., Comment: Accepted in Phys. Rev. E. 15 pages. arXiv admin note: text overlap with arXiv:2309.05207

In the microcanonical thermal pure quantum (mTPQ) method, the canonical ensemble is derived using Taylor series expansions. We prove that the truncation error decreases exponentially with system size when the effective temperature of the mTPQ state is smaller than the target temperature, and otherwise, the error remains constant. We also show the discipline to set the mTPQ parameter by considering the trade-off between the error and the numerical cost., Comment: 2 pages

Correlations of the displacement field in a two-dimensional model colloidal liquid is studied numerically and analytically. By calculating the displacement correlations and the shear strain correlations from the numerical data of particle simulations, the displacement field is shown to have nontrivial correlations, even in liquids that are only slightly glassy with the area fraction as low as 0.5. It is suggested analytically and demonstrated numerically that the displacement correlations are more informative than the shear correlations: the former behaves logarithmically with regard to the spatial distance at shorter scales, while the corresponding information is missing from the shear correlations. The logarithmic behavior of the displacement correlations is interpreted as manifesting a long-lived aspect of the cage effect., Comment: 24 pages, 15 figures; submitted to Physical Review E

The hydrodynamics of crystals with vacancies is developed on the basis of local-equilibrium thermodynamics, where the chemical potential of vacancies plays a key role together with a constraint relating the concentration of vacancies to the density of mass and the strain tensor. The microscopic foundations are established, leading to Green-Kubo and Einstein-Helfand formulas for the transport coefficients, including the vacancy conductivities and the coefficients of vacancy thermodiffusion. As a consequence of having introduced the chemical potential of vacancies, a relationship is obtained between the conductivities and the Fickian diffusion coefficients for the vacancies. The macroscopic equations are linearized around equilibrium to deduce the dispersion relations of the eight hydrodynamic modes. The theoretical predictions are confirmed by numerical simulations of the hard-sphere crystal with vacancies. The study explicitly shows that the eighth hydrodynamic mode of nonperfect monatomic crystals is indeed a mode of vacancy diffusion., Comment: 24 pages, 6 figures, 8 tables

Critical single-particle fluctuations associated with particle displacements are inherent to simple glass-forming liquids in the limit of large dimensions and leave a pseudo-critical trace across all finite dimensions. This characteristic could serve as a crucial test for distinguishing between theories of glass formation. We here examine these critical fluctuations, as captured by the well-established non-Gaussian parameter, within both mode-coupling theory (MCT) and dynamical mean-field theory (DMFT) across dimensions for hard sphere liquids and for the minimally structured Mari--Kurchan model. We establish general scaling laws relevant to any liquid dynamics theory in large dimensions and show that the dimensional scalings predicted by MCT are inconsistent with those from DMFT. Simulation results for hard spheres in moderately high dimensions align with the DMFT scenario, reinforcing the relevance of mean-field theory for capturing glass physics in finite dimensions. We identify potential adjustments to MCT to account for certain mean-field physics. Our findings also highlight that local structure and spatial dimensionality can affect single-particle critical fluctuations in non-trivial ways., Comment: 42 pages, 9 figures

Shortcuts to adiabaticity are strategies for conserving adiabatic invariants under non-adiabatic (i.e. fast-driving) conditions. Here, we show how to extend classical, Hamiltonian shortcuts to adiabaticity to allow the crossing of a phase-space separatrix -- a situation in which a corresponding adiabatic protocol does not exist. Specifically, we show how to construct a time-dependent Hamiltonian that evolves one energy shell to another energy shell across a separatrix. Leveraging this method, we design an erasure procedure whose energy cost and fidelity do not depend on the protocol's duration.

We numerically investigate two-dimensional systems of hard rectangles at constant pressure through extensive hard-particle Monte Carlo simulations. We determine the complete phase diagram as a function of packing fraction and aspect ratio, which consists of four distinct phases. At very high packing fractions, particles form a smectic solid for all aspect ratios. Rod-like particles with large aspect ratio assemble in an intervening nematic phase, which is displaced by a "tetratic" phase (also called biaxial nematic) for moderately elongated rectangles. Surprisingly, we find evidence that the transition from tetratic to smectic is weakly discontinuous at variance with previously proposed two-step scenarios for the melting of hard particles.

We study the excitation spectrum of the $S=1/2$ Heisenberg model on the randomly diluted square lattice by analytic continuation of QMC data. At dilution fractions $p=1/16$ and $p=1/8$, the dynamic structure factor $S({\bf q},\omega)$ exhibits a damped magnon peak with anomalous dispersion near ${\bf q}=(0,0)$ and $(\pi,\pi)$, a non-dispersive low-energy localization peak, and a second dispersive peak between these two features. A magnon with anomalous dispersion, close to our result, was predicted in spin wave and $T$-matrix theory [A. Chernyshev et al., PRB {\bf 65}, 104407 (2002)], above the localization energy. However, no intermediate dispersive mode was predicted. Analyzing spectral functions in real space for individual vacancy realizations by energy tomography, we find that these excitations are concentrated on a small subset of the spins adjacent to vacancies. We argue that the low-energy excitations are those of a sparse random network of effective moments at a fraction of the vacancies. There is a shift in magnon spectral weight distribution, from the spins away from vacancies at high energy to those adjacent to vacancies at lower energy. We also analyze the Anderson quantum rotor excitation at $\omega \propto N^{-1}$ (with $N=L^2$ the system size), which in the clean system is visible in $S({\bf q},\omega)$ only at ${\bf q}=(\pi,\pi)$ but spreads through the Brillouin zone when $p>0$. Weight close to ${\bf q}=(0,0)$ and $(\pi,\pi)$ is explained by local sublattice imbalance within a dimer-monomer model but there is also structure arising from correlated singlet fluctuations, which we demonstrate by enhancing said fluctuations with four-spin couplings. All spectral features found here should be observable by elastic neutron scattering experiments on layered quantum antiferromagnets doped with nonmagnetic impurities., Comment: 35 pages, 37 figures

We experimentally investigate the statistical properties of the quantum analog of entanglement between two electric circuits equivalent to two Brownian particles connected by an elastic force and maintained at different temperatures through separate heat reservoirs. Uncertainty relations between coordinates and coarse-grained velocity can produce a phenomenon similar to quantum entanglement, where temperature plays the role of Planck's constant. The theoretical analysis matches the experimental results, confirming that the interconnected particles exhibit Brownian quantum-inspired classical correlation entanglement. This effect arises from a coarse grained description of Brownian motion and vanishes at a finer resolution. {The coarsening scales range is measured too., Comment: 12 pages + 4 pages Supplementary Material

Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure., Comment: 63 pages, 47 figures

We use a space-time discretization based on physics informed deep learning (PIDL) to approximate solutions of a class of rate-dependent strain gradient plasticity models. The differential equation governing the plastic flow, the so-called microforce balance for this class of yield-free plasticity models, is very stiff, often leading to numerical corruption and a consequent lack of accuracy or convergence by finite element (FE) methods. Indeed, setting up the discretized framework, especially with an elaborate meshing around the propagating plastic bands whose locations are often unknown a-priori, also scales up the computational effort significantly. Taking inspiration from physics informed neural networks, we modify the loss function of a PIDL model in several novel ways to account for the balance laws, either through energetics or via the resulting PDEs once a variational scheme is applied, and the constitutive equations. The initial and the boundary conditions may either be imposed strictly by encoding them within the PIDL architecture, or enforced weakly as a part of the loss function. The flexibility in the implementation of a PIDL technique often makes for its ready interface with powerful optimization schemes, and this in turn provides for many possibilities in posing the problem. We have used freely available open-source libraries that perform fast, parallel computations on GPUs. Using numerical illustrations, we demonstrate how PIDL methods could address the computational challenges posed by strain gradient plasticity models. Also, PIDL methods offer abundant potentialities, vis-\'a-vis a somewhat straitjacketed and poorer approximant of FE methods, in customizing the formulation as per the problem objective.

Distribution functions of collisionless systems are known to show non-thermal power law tails. Interestingly, collisionless plasmas in various physical scenarios, (e.g., the ion population of the solar wind) feature a $v^{-5}$ tail in the velocity ($v$) distribution, whose origin has been a long-standing mystery. We show this power law tail to be a natural outcome of the self-consistent collisionless relaxation of driven electrostatic plasmas. We perform a quasilinear analysis of the perturbed Vlasov-Poisson equations to show that the coarse-grained mean distribution function (DF), $f_0$, follows a quasilinear diffusion equation with a diffusion coefficient $D(v)$ that depends on $v$ through the plasma dielectric constant. If the plasma is isotropically forced on scales much larger than the Debye length with a white noise-like electric field, then $D(v)\sim v^4$ for $\sigma

Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method can dramatically reduce the computational effort. We apply the method to two test problems, namely a simple model Hamiltonian and to a more realistic Hamiltonian for nuclear fission. For a Hamiltonian of dimension 66103 we find that the computation time is reduced by a factor of 33 compared to the direct calculation of the Green's function., Comment: 8 pages, 4 figures, 1 table

We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical properties by performing Monte Carlo simulations on relatively small system sizes. We demonstrate this method on the XY model in three dimensions. Our method may provide a framework with which to efficiently study universal properties in a large class of phase transitions., Comment: 20 pages, 20 figures

We numerically study the evolution of a classical real scalar field in ${(1+1)}$ dimensions with initial conditions describing thermal fluctuations around a metastable vacuum. We track false vacuum decay in real time and compare several observables to the predictions of the standard Euclidean formalism. We find agreement for the shape of the critical bubble and the exponential suppression of the decay rate. However, the decay rate prefactor is almost an order of magnitude lower than the predicted value. We argue that this signals a breakdown of thermal equilibrium during the bubble nucleation. In addition, the inefficient thermalization in the system biases the properties of the statistical ensemble and leads to further decrease of the decay rate with time. We substantiate our interpretation with a suite of stochastic field simulations with controlled thermalization time. Varying this time we find that the predictions of the standard equilibrium formalism are recovered when it is sufficiently short. We propose an upper bound on the thermalization time that must be satisfied in order to ensure the applicability of the Euclidean rate calculation. We discuss that this bound is unavoidably violated in common single-field models, irrespective of the number of spacetime dimensions, implying that deviations from equilibrium in these models cannot be neglected. In theories with multiple fields, the bound may or may not hold, depending on the setup details. We investigate one more signature of non-equilibrium dynamics -- coherent oscillonic precursors to the critical bubble nucleation. We show that they get suppressed in the stochastic dynamical simulations when the thermalization time is reduced., Comment: 50 pages, 19 figures

We study Ruelle-Pollicott resonances in translationally invariant quantum many-body systems via spectra of momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into decay of correlation functions, showing that, depending on their symmetries, different correlation functions in general decay with different rates. Focusing on the kicked Ising model the spectrum seems to be typically composed of an annular random matrix like ring whose size we theoretically predict, and few isolated resonances. We identify several interesting regimes, including a mixing regime with a power-law decay of correlation functions. In that regime we also observe a huge difference in time-scales of different correlation functions. An exact expression for the singular values of the operator propagator is conjectured, showing that it becomes singular at a special point., Comment: 12 pages

Proposed as an elegant symmetry relating bosons and fermions, spacetime supersymmetry (SUSY) has been actively pursued in both particle physics and emergent phenomena in quantum critical points (QCP) of topological quantum materials. However, how SUSY casts the light on nonequilibrium dynamics remains open. In this letter, we investigate the Kibble-Zurek dynamics across a QCP with emergent $\mathcal{N}=2$ spacetime SUSY between the Dirac semimetal and a superconductor through large-scale quantum Monte Carlo simulation. The scaling behaviors in the whole driven process are uncovered to satisfy the full finite-time scaling (FTS) forms. More crucially, we demonstrate that the emergent SUSY manifests in the intimate relation between the FTS behaviors of fermionic and bosonic observables, namely the fermions and bosons acquire the identical anomalous dimensions. Our work not only brings a fundamental new ingredient into the critical theory with SUSY, but also provide the theoretical guidance to experimental detect of QCP with emergent SUSY from the perspectives of Kibble-Zurek mechanism and FTS., Comment: 7+2 pages, 3 figures

One of quantum physics's fundamental, but largely unsolved, problems is the computation of the correlation functions in many-body systems. In this paper we address this problem in the case of one-dimensional spinor gases with repulsive contact interactions in the presence of a confining potential. We take advantage of the fact that in the strong coupling limit, the wavefunction factorizes with the charge degrees of freedom expressed as a Slater determinant of spinless fermions and the spin sector described by a spin chain of Sutherland type with exchange coefficients that depend only on the trapping potential. This factorization is also present in the expressions for the correlation functions. Still, analytical and numerical investigations were hindered by the fact that the local exchange coefficients and the charge component of the correlators are expressed as $N-1$ multidimensional integrals, with $N$ the number of particles, which are notoriously hard to compute using conventional methods. We introduce a new approach to calculating these integrals that is extremely simple, scales polynomially with the number of particles, and is several orders of magnitude faster than the previous methods reported in the literature. This allows us to investigate the static and dynamic properties, temperature dependence, and nonequilibrium dynamics for systems with larger number of particles than previously considered and discover new phenomena. We show that, contrary to natural expectations, the momentum distribution of strongly interacting trapped spinor gases becomes narrower as we increase the temperature and derive simple determinant representations for the correlators in the spin incoherent regime valid for both equilibrium and nonequilibrium situations., Comment: 24 pages, 6 figures, RevTeX 4.2

The probability that a configuration of a physical system reacts, or transitions from one metastable state to another, is quantified by the committor function. This function contains richly detailed mechanistic information about transition pathways, but a full parameterization of the committor requires building representing a high-dimensional function, a generically challenging task. Recent efforts to leverage neural networks as a means to solve high-dimensional partial differential equations, often called "physics-informed" machine learning, have brought the committor into computational reach. Here, we build on the semigroup approach to learning the committor and assess its utility for predicting dynamical quantities such as transition rates. We show that a careful reframing of the objective function and improved adaptive sampling strategies provide highly accurate representations of the committor. Furthermore, by directly applying the Hill relation, we show that these committors provide accurate transition rates for molecular system.

On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar states manifest themselves as super uidity and superconductivity., Comment: 5 pages

Quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QW with the conventional, symmetric, and split-step translation operators with or without classical randomness in the coin operator, we show the entanglement is robust against both time- and spatially- dependent randomness, which can cause localization transitions of QW. We propose a classical quantity call overlap, which literally measures the overlap between the probability distributions of the internal states, as a proxy of entanglement. The overlap captures the inverse behavior of the entanglement entropy in most cases, which can be explained by analyzing the structure of the total wave function of the walker. We test the limitation of the classical proxy by constructing a special case with high population imbalance between the internal states to blind the overlap. Possible implications and experimental measurements are also discussed., Comment: 13 pages, 10 figures

Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are suitable quantities essentially free from basis dependence. The complexity is defined as the difference between the Shannon-entropy and the second order R\'enyi-entropy, where the latter is connected to the traditional participation measure or purity. It is shown that the system attains maximal complexity for special choice of control parameters, i.e. strength of disorder either in the presence of noise of the energy states or the presence of disorder in the off diagonal coupling. It is shown that such a noise or disorder dependence provides a basis free analysis and gives meaningful insights. We also look at similar entropic complexity of spins in thermal equilibrium for a paramagnet at finite temperature, $T$ and magnetic field $B$, as well as the case of an Ising model in the mean-field approximation. As a result all examples provide important evidence that the investigation of the entropic complexity parameters help to get deeper understanding in the behavior of these systems., Comment: 8 pages, 9 figures

The standard definition of particle number fluctuations based on point-like particles neglects the excluded volume effect. This leads to a large and systematic finite-size scaling and an unphysical surface term in the isothermal compressibility. We correct these errors by introducing a modified pair distribution function which takes account of the finite size of the particles. For the hard sphere fluid in one-dimension, we show that the compressibility is strictly size-independent and we reproduce this result from the number fluctuations calculated with the new theory. In general, the present method eliminates the leading finite-size effect, which makes it possible to compute density fluctuations accurately in very small sampling volumes, comparable to the single particle size. These findings open the way for obtaining local response functions from fluctuation theory at the nanometer scale., Comment: 8 pages, 4 figures

The geometry of quantum states could offer indispensable insights for characterizing the topological properties, phase transitions and entanglement nature of many-body systems. In this work, we reveal the quantum geometry and the associated entanglement entropy (EE) of Floquet topological states in one-dimensional periodically driven systems. The quantum metric tensors of Floquet states are found to show non-analytic signatures at topological phase transition points. Away from the transition points, the bipartite geometric EE of Floquet states exhibits an area-law scaling vs the system size, which holds for a Floquet band at any filling fractions. For a uniformly filled Floquet band, the EE further becomes purely quantum geometric. At phase transition points, the geometric EE scales logarithmically with the system size and displays cusps in the nearby parameter ranges. These discoveries are demonstrated by investigating typical Floquet models including periodically driven spin chains, Floquet topological insulators and superconductors. Our findings uncover the rich quantum geometries of Floquet states, unveiling the geometric origin of EE for gapped Floquet topological phases, and introducing information-theoretic means of depicting topological transitions in Floquet systems., Comment: 18 pages, 6 figures, version accepted by PRB

Common wisdom dictates that physical systems become less ordered when heated to higher temperature. However, several systems display the opposite phenomenon and move to a more ordered state upon heating, e.g. at low temperature piezoelectric quartz is paraelectric and it only becomes piezoelectric when heated to sufficiently high temperature. The presence, or better, the re-entrance of unordered phases at low temperature is more prevalent than one might think. Although specific models have been developed to understand the phenomenon in specific systems, a universal explanation is lacking. Here we propose a universal simple microscopic theory which predicts the existence of two critical temperatures in inhomogeneous systems, where the lower one marks the re-entrance into the less ordered phase. We show that the re-entrant phase transition is caused by disorder-induced spatial localization of the zero-mode on a finite, i.e. sub-extensive, region of the system. Specifically, this trapping of the zero-mode disconnects the fluctuations of the order parameter in distant regions of the system, thus triggering the loss of long-range order and the re-entrance into the disordered phase. This makes the phenomenon quite universal and robust to the underlying details of the model, and explains its ubiquitous observation., Comment: 26 pages, 9 figures

The study of open system dynamics is of paramount importance both from its fundamental aspects as well as from its potential applications in quantum technologies. In the simpler and most commonly studied case, the dynamics of the system can be described by a Lindblad master equation. However, identifying the Lindbladian that leads to general non-equilibrium steady states (NESS) is usually a non-trivial and challenging task. Here we introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS, i.e., a Lindbladian Reverse Engineering ($\mathcal{L}$RE) approach. The method maps the reconstruction task to a simple linear problem. Specifically, to the diagonalization of a correlation matrix whose elements are NESS observables and whose size scales linearly (at most quadratically) with the number of terms in the Hamiltonian (Lindblad jump operator) ansatz. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. Moreover, the map defines an iff condition for $\mathcal{L}$RE, which works as both a necessary and a sufficient condition; thus, it not only defines, if possible, Lindbaldian evolutions leading to the target NESS, but also determines the feasibility of such evolutions in a proposed setup. We illustrate the method in different systems, ranging from bosonic Gaussian to dissipative-driven collective spins. We also discuss non-Markovian effects and possible forms to recover Markovianity in the reconstructed Lindbaldian., Comment: 11 pages, 7 figures

We present a mathematical theory of metastable pure states in closed many-body quantum systems with finite-dimensional Hilbert space. Given a Hamiltonian, a pure state is defined to be metastable when all sufficiently local operators either stabilize the state, or raise its average energy. We prove that short-range entangled metastable states are necessarily eigenstates (scars) of a perturbatively close Hamiltonian. Given any metastable eigenstate of a Hamiltonian, in the presence of perturbations, we prove the presence of prethermal behavior: local correlation functions decay at a rate bounded by a time scale nonperturbatively long in the inverse metastability radius, rather than Fermi's Golden Rule. Inspired by this general theory, we prove that the lifetime of the false vacuum in certain $d$-dimensional quantum models grows at least as fast as $\exp(\epsilon^{-d} \log^{-3} \epsilon^{-1} )$, where $\epsilon\rightarrow 0$ is the relative energy density of the false vacuum; up to logarithms, this lower bound matches, for the first time, explicit calculations using quantum field theory. We identify metastable states at finite energy density in the PXP model, along with exponentially many metastable states in "helical" spin chains and the two-dimensional Ising model. Our inherently quantum formalism reveals precise connections between many problems, including prethermalization, robust quantum scars, and quantum nucleation theory, and applies to systems without known semiclassical and/or field theoretic limits., Comment: 26+34 pages; 6+3 figures