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Path-integral molecular dynamics (PIMD) simulations are crucial for accurately capturing nuclear quantum effects in materials. However, their computational intensity and reliance on multiple software packages often limit their applicability at large scales. Here, we present an integration of PIMD methods, including thermostatted ring-polymer molecular dynamics (TRPMD), into the open-source GPUMD package, combined with highly accurate and efficient machine-learned neuroevolution potential (NEP) models. This approach achieves almost the accuracy of first-principles calculations with the computational efficiency of empirical potentials, enabling large-scale atomistic simulations that incorporate nuclear quantum effects. We demonstrate the efficacy of the combined NEP-PIMD approach by examining various thermal properties of diverse materials, including lithium hydride (LiH), three porous metal-organic frameworks (MOFs), and elemental aluminum. For LiH, our NEP-PIMD simulations successfully capture the isotope effect, reproducing the experimentally observed dependence of the lattice parameter on the reduced mass. For MOFs, our results reveal that achieving good agreement with experimental data requires consideration of both nuclear quantum effects and dispersive interactions. For aluminum, the TRPMD method effectively captures thermal expansion and phonon properties, aligning well with quantum mechanical predictions. This efficient NEP-PIMD approach opens new avenues for exploring complex material properties influenced by nuclear quantum effects, with potential applications across a broad range of materials., Comment: 14 pages, 6 figures in the main text; 1 table and 5 figures in the SI

Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral atom quantum computers will suffer from correlated errors because of the finite lifetime of the Rydberg states that facilitate entanglement. Predicting the impact of such errors on the performance of topological QEC codes is important in understanding and characterising the fidelity limitations of a real quantum device. Mapping a QEC code to a $\mathbb{Z}_2$ lattice gauge theory with disorder allows us to use Monte Carlo techniques to calculate upper bounds on error rates without resorting to an optimal decoder. In this Article, we adopt this statistical mapping to predict error rate thresholds for neutral atom architecture, assuming radiative decay to the computational basis, leakage and atom loss as the sole error sources. We quantify this error rate threshold $p_\text{th}$ and bounds on experimental constraints, given any set of experimental parameters., Comment: 9 figures, 16 pages

We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent for the investigation of confinement-induced effects. We analytically derive exact results for the characteristic function of the moments valid to first order in the obstacle density. By calculating the velocity autocorrelation function and its long-time tail we find that already in equilibrium the system exhibits a dimensional crossover. This picture is further confirmed by the approach of the drift velocity to its terminal value attained in the non-equilibrium stationary state. At large times the diffusion coefficient is affected by both the driving and confinement in a way that we quantify analytically. The force-induced diffusion coefficient depends sensitively on the presence of confinement. The latter is able to modify qualitatively the non-analytic behavior in the force observed for the unbounded model. We then examine the fluctuations of the tracer particle along the driving force. We show that in the intermediate regime superdiffusive anomalous behavior persists even in the presence of confinement. Stochastic simulations are employed in order to test the validity of the analytic results, exact to first order in the obstacle density and valid for arbitrary force and confinement., Comment: 24 pages, 7 figures

We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size., Comment: 6 pages, 3 figures

Chemotactic biological or synthetic active matter shapes its environment by secretions of chemical signals from its self-propelled constituents, like cells, organisms or active colloids. From this indirect interaction collective effects emerge that can be used by the agents to migrate collectively, to form patterns or to search for targets more efficiently. Here, we use paradigmatic models to study the efficiency of collective search strategies of a large group of motile agents that release during their movement repulsive auto-chemotactic signals forcing them to move away from high concentrations of the chemical clue. We show that the repulsive chemotactic interactions improve the search efficiency, measured by the mean first passage time to find a randomly located target, by orders of magnitude depending on the strength of the chemotactic coupling. The mechanism for this improvement relies on two factors: the increase of the persistence length due to the agent's self-interaction with its own chemotactic field and by a more homogeneous distribution of the agents due to their mutual indirect repulsion mediated by the chemotactic field. At stronger particle-field coupling the chemotactic searchers self-organize into ballistically moving bands reminiscent of search-chains formed in search and rescue operations, whose efficiency depends on the number of searchers involved. Our comprehensive study of collective search strategies of large groups of interacting agents is not only relevant for chemotactic active matter but also for a wide range of fields like ethology, information engineering, robotics, and social engineering., Comment: 15 pages, 11 figures

Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to molecular self-diffusion in fluids. The foundational principles of Gaussianity and Markovianity, central to the Brownian diffusion paradigm, are insufficient for describing molecular diffusion, particularly in complex fluids characterized by intricate intermolecular interactions and hindered relaxation processes. This perspective delves into the nuanced behavior observed in diverse complex fluids, including molecular self-assembly, deep eutectic solvents, and ionic liquids, with a specific focus on modeling self-diffusion within these media. We explore the potential of extending diffusion models to incorporate non-Gaussian and non-Markovian effects by augmenting the Brownian model using non-local diffusion equations. Further, we validate the applicability of these models by utilizing them to describe results from quasielastic neutron scattering and MD simulations.

The Master Stability Function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic dynamical systems, its application to periodic systems has been less explored. By studying several well-known periodic systems, we establish a comprehensive framework to understand and classify their properties of synchronizability. This allows us to define five distinct classes of synchronization stability, including some that are unique to periodic systems. Specifically, in periodic systems, the Master Stability Function vanishes at the origin, and it can therefore display behavioral classes that are not achievable in chaotic systems, where it starts, instead, at a strictly positive value. Moreover, our results challenge the widely-held belief that periodic systems are easily put in a stable synchronous state, showing, instead, the common occurrence of a lower threshold for synchronization stability., Comment: 8 pages, 6 figures, plus supplementary material with 5 pages and 6 figures

Non-equilibrium clustering and percolation are investigated in an archetypal model of two-dimensional active matter using dynamic simulations of self-propelled Brownian repulsive particles. We concentrate on the single-phase region up to moderate levels of activity, before motility-induced phase separation (MIPS) sets in. Weak activity promotes cluster formation and lowers the percolation threshold. However, driving the system further out of equilibrium partly reverses this effect, resulting in a minimum in the critical density for the formation of system-spanning clusters and introducing re-entrant percolation as a function of activity in the pre-MIPS regime. This non-monotonic behaviour arises from competition between activity-induced effective attraction (which eventually leads to MIPS) and activity-driven cluster breakup. Using an adapted iterative Boltzmann inversion method, we derive effective potentials to map weakly active cases onto a passive (equilibrium) model with conservative attraction, which can be characterised by Monte Carlo simulations. While the active and passive systems have practically identical radial distribution functions, we find decisive differences in higher-order structural correlations, to which the percolation threshold is highly sensitive. For sufficiently strong activity, no passive pairwise potential can reproduce the radial distribution function of the active system.

Three types of cycles are identified in the quantum jump trajectories of the Scovil--Schulz-DuBois (SSDB) machine: an R-cycle as refrigeration, an H-cycle as a heat engine, and an N-cycle in which the machine is neutral. The statistics of these cycles are investigated via a semi-Markov process method. We find that in the large time limit, whether the machine operates as a heat engine or refrigerator depends on a balance between the numbers of R-cycles and H-cycles per unit time. Further increasing the hot bath temperature above a certain threshold does not increase the machine's power output. The cause is that, in this situation, the N-cycle has a greater probability than the H-cycle and R-cycle. Although the SSDB machine operates by randomly switching among these three cycles, at the level of a single quantum jump trajectory, its heat engine efficiency and the refrigerator's coefficient of performance remain constant., Comment: 3 figures

Pyrochlore magnets have proven to provide an excellent arena for the realization of a variety of many-body phenomena such as classical and quantum order-by-disorder, as well as spin liquid phases described by emergent gauge field theories. These phenomena arise from the competition between different symmetry-breaking magnetic orders. In this work, we consider a subspace of the most general bilinear nearest-neighbor Hamiltonian on the pyrochlore lattice, parameterized by the local interaction parameter $J_{z\pm}$, where three symmetry-breaking phases converge. We demonstrate that for small values of $|J_{z\pm}|$, a conventional $\mathbf q=0$ ordered phase is selected by a thermal order-by-disorder mechanism. For $|J_{z\pm}|$ above a certain finite threshold, a novel spin-nematic phase is stabilized at low temperatures. Instead of the usual Bragg peaks, the spin-nematic phase features lines of high intensity in the spin structure factor. At intermediate temperatures above the low-temperature orders, a rank-2 U(1) classical spin liquid is realized for all $J_{z\pm} \neq 0$. We fully characterize all phases using classical Monte-Carlo simulations and a self-consistent Gaussian approximation., Comment: 17 pages, 17 figures

We examine the connection between deep learning and information theory through the paradigm of diffusion models. Using well-established principles from non-equilibrium thermodynamics we can characterize the amount of information required to reverse a diffusive process. Neural networks store this information and operate in a manner reminiscent of Maxwell's demon during the generative stage. We illustrate this cycle using a novel diffusion scheme we call the entropy matching model, wherein the information conveyed to the network during training exactly corresponds to the entropy that must be negated during reversal. We demonstrate that this entropy can be used to analyze the encoding efficiency and storage capacity of the network. This conceptual picture blends elements of stochastic optimal control, thermodynamics, information theory, and optimal transport, and raises the prospect of applying diffusion models as a test bench to understand neural networks., Comment: 37 pages + references, 11 figures

We begin with an exact expression for the entropy of a system of hard spheres within the Hamming space. This entropy relies on probability marginals, which are determined by an extended set of Belief Propagation (BP) equations. The BP probability marginals are functions of auxiliary variables which are introduced to model the effects of loopy interactions on a tree-structured interaction graph. We explore various reasonable and approximate probability distributions, ensuring they align with the exact solutions of the BP equations. Our approach is based on an ansatz of (in)homogeneous cavity marginals respecting the permutation symmetry of the problem. Through thorough analysis, we aim to minimize errors in the BP equations. Our findings support the conjecture that the maximum packing density asymptotically conforms to the lower bound proposed by Gilbert and Varshamov, further validated by the solution of the loopy BP equations., Comment: 31 pages, 4 figures

Quantum complexity has emerged as a central concept in diverse areas of physics, ranging from quantum computing to the theory of black holes. We perform a systematic study of complexity in random quantum circuits with and without measurements. We observe that complexity grows linearly before saturating to a constant value. For $N$ qubits without measurements, the saturation value scales as $2^{N-1}$, and the saturation time scales as $2^N$. This behaviour remains identical in the presence of random measurements with different probabilities, indicating that this notion of complexity is insensitive to the rate of measurement. We also study the behaviour of complexity in two variants of the random unitary floquet circuit, where we observe that complexity acts as a novel probe of Anderson localization and many-body localization., Comment: 6 pages, 3 figures

We consider the three-dimensional (3D) lattice SU($N_c$) gauge Higgs theories with multicomponent ($N_f>1$) degenerate scalar fields and U($N_f$) global symmetry, focusing on systems with $N_c=2$, to identify critical behaviors that can be effectively described by the corresponding 3D SU($N_c$) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of $N_f$, that would control transitions characterized by the global symmetry-breaking pattern ${\rm U}(N_f)\rightarrow \mathrm{SU}(2)\otimes \mathrm{U}(N_f-2)$. Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for $N_f \ge 30$. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of $N_f$. The results are in substantial agreement with the field-theoretical predictions obtained in the large-$N_f$ limit. This provides evidence that the SU($N_c$) gauge Higgs field theories provide the correct effective description of the 3D large-$N_f$ continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to $\mathrm{SU}(2)\otimes \mathrm{U}(N_f-2)$. Therefore, at least for large enough $N_f$, the 3D SU($N_c$) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretizatized models with the same local and global symmetries., Comment: 10 pages, 8 pdf figures

In this note, the equilibrium curve of a thermodynamic system is used to depict entropy production in the process of thermalization with a reservoir. For the given initial and final equilibrium states of the system, the entropy production is reduced when work is also extracted during thermalization. The case of maximum work extraction corresponds to a reversible process. For less than optimal work extraction, the lost available work is shown to be directly proportional to the entropy produced., Comment: 5 pages, 2 figures

The motility of living things and synthetic self-propelled objects is often described using Active Brownian particles. To capture the interaction of these particles with their often complex environment, this model can be augmented with empirical forces or torques, for example, to describe their alignment with an obstacle or wall after a collision. Here, we assess the quality of these empirical models by comparing their output predictions with trajectories of rod-shaped active particles that scatter sterically at a flat wall. We employ a classical least-squares method to evaluate the instantaneous torque. In addition, we lay out a Bayesian inference procedure to construct the posterior distribution of plausible model parameters. In contrast to the least squares fit, the Bayesian approach does not require orientational data of the active particle and can readily be applied to experimental tracking data.

The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of the system. The associated BBGKY hierarchy of equations for the reduced distribution functions is expanded in powers of a parameter measuring the density of the system in the appropriate dimensionless units. The Boltzmann level of description is obtained by keeping only the two lowest orders in the parameter. In particular, the one-particle distribution function obeys a couple of equations. Contrary to what happens with a Boltzmann-like kinetic equation that has been proposed for the same system on a heuristic basis, the kinetic theory formulated here admits stationary solutions that are consistent with equilibrium statistical mechanics, both in absence and presence of external fields. In the latter case, the density profile is rather complex due to the coupling between the inhomogeneities generated by the confinement and by the external fields. The general theory formulated provides a solid basis for the study of the properties of strongly confined dilute gases., Comment: Accepted in Physical Review E

The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. In this work, we study effects of non-uniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatio-temporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code., Comment: 22 pages, 17 figures

We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a power-law in the distance between particles, with a tunable exponent. Such long-range processes arise naturally in various classical settings, such as chemical reactions involving reagents with long-range electromagnetic interactions. They also increasingly play a role in the study of quantum dynamics, in which certain quantum protocols can be mapped to classical stochastic processes with long-range interactions: for example, state preparation or error correction processes aim to prepare ordered ground states, which requires removing point-like excitations in pairs via non-local feedback operations conditioned on a global set of measurement outcomes. We analytically and numerically describe features of absorbing phases and phase transitions in this family of classical models as pairwise annihilation is performed at larger and larger distances. Notably, we find that the two canonical absorbing-state universality classes -- directed-percolation and parity-conserving -- are endpoints of a line of universality classes with continuously interpolating critical exponents., Comment: 5+8 pages, 3 figures

This paper deals with themes such as approximate counting/evaluation of the total number of flat-foldings for random origami diagrams, evaluation of the values averaged over various instances, obtaining forcing sets for general origami diagrams, and evaluation of average computational complexity. An approach to the above problems using a physical model and an efficient size reduction method for them is proposed. Using a statistical mechanics model and a numerical method of approximate enumeration based on it, we give the result of approximate enumeration of the total number of flat-foldings of single-vertex origami diagram with random width of angles gathering around the central vertex, and obtain its size dependence for an asymptotic prediction towards the limit of infinite size. In addition, an outlook with respect to the chained determination of local stacking orders of facets caused by the constraint that prohibits the penetration of them is also provided from the viewpoint of organizing the terms included in the physical model. A method to efficiently solve the problem of the determination or enumeration of flat-foldings is discussed based on the above perspectives. This is thought to be closely related to forcing sets., Comment: 16 pages, 11 figures. Submitted to Origami8: Proceedings of the 8th International Meeting on Origami in Science, Mathematics and Education (8OSME), Melbourne, August 16-18, 2024

The recent surge in Generative Artificial Intelligence (AI) has introduced exciting possibilities for computational chemistry. Generative AI methods have made significant progress in sampling molecular structures across chemical species, developing force fields, and speeding up simulations. This Perspective offers a structured overview, beginning with the fundamental theoretical concepts in both Generative AI and computational chemistry. It then covers widely used Generative AI methods, including autoencoders, generative adversarial networks, reinforcement learning, flow models and language models, and highlights their selected applications in diverse areas including force field development, and protein/RNA structure prediction. A key focus is on the challenges these methods face before they become truly predictive, particularly in predicting emergent chemical phenomena. We believe that the ultimate goal of a simulation method or theory is to predict phenomena not seen before, and that Generative AI should be subject to these same standards before it is deemed useful for chemistry. We suggest that to overcome these challenges, future AI models need to integrate core chemical principles, especially from statistical mechanics.

Biological functionality of cellular aggregates is largely influenced by the activity and displacements of individual constituent cells. From a theoretical perspective this activity can be characterized by hydrodynamic transport coefficients of diffusivity and conductivity. Motivated by the clustering dynamics of bacterial microcolonies we propose a model of active multicellular aggregates and use recently developed macroscopic fluctuation theory to derive a fluctuating hydrodynamics for this model system. Both semi-analytic theory and microscopic simulations show that the hydrodynamic transport coefficients are affected by non-equilibrium microscopic parameters and significantly decrease inside of the clusters. We further find that the Einstein relation connecting the transport coefficients and fluctuations breaks down in the parameter regime where the detailed balance is not satisfied. This study offers valuable tools for experimental investigation of hydrodynamic transport in other systems of cellular aggregates such as tumor spheroids and organoids.

We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension $\sim 5$ with $N=16$ fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets., Comment: 31 pages, 13 figures

Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface whose period is $\tau=\hbar /(k_{\mathrm{B}}T)$. Unfortunately, the standard theory is only applicable below the "crossover temperature", where the periodic orbit first appears. This paper presents a rigorous semiclassical ($\hbar\to0$) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation function derivation of instanton theory. The resulting theory smoothly connects the instanton result at low temperature to the parabolic correction to Eyring transition state theory at high-temperature. Although the derivation involves real time, the final theory only involves imaginary-time (thermal) properties, consistent with the standard theory. Therefore, it is no more difficult to compute than the standard theory. The theory is illustrated with application to model systems, where it is shown to give excellent numerical results. Finally, the first-principles approach taken here results in a number of advantages over previous attempts to extend the imaginary free-energy formulation of instanton theory. In addition to producing a theory that is a smooth (continuously differentiable) function of temperature, the derivation also naturally incorporates hyperasymptotic (i.e.~multi-orbit) terms, and provides a framework for further extensions of the theory., Comment: 26 pages, 6 figures

We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasi-polynomial runtime for inverse temperatures up to $\beta={\rm poly}(\ln(n))$. At the core of our approach is the Density Matrix Renormalization Group algorithm, which typically does not guarantee efficiency. We have created a new truncation scheme for the matrix product operator of the quantum Gibbs states, which allows us to control the error analytically. Additionally, our method is applied to simulate the time evolution of systems with long-range interactions, achieving significantly better precision than that offered by the Lieb-Robinson bound., Comment: 7 pages + 9 pages Supplementary materials, 1 figure

The dynamics of electric power systems are widely studied through the phase synchronization of oscillators, typically with the use of the Kuramoto equation. While there are numerous well-known order parameters to characterize these dynamics, shortcoming of these metrics are also recognized. To capture all transitions from phase disordered states over phase locking to fully synchronized systems, new metrics were proposed and demonstrated on homogeneous models. In this paper we aim to address a gap in the literature, namely, to examine how gradual improvement of power grid models affect the goodness of certain metrics. To study how the details of models are perceived by the different metrics, 12 variations of a power grid model were created, introducing varying level of heterogeneity through the coupling strength, the nodal powers and the moment of inertia. The grid models were compared using a second-order Kuramoto equation and adaptive Runge-Kutta solver, measuring the values of the phase, the frequency and the universal order parameters. Finally, frequency results of the models were compared to grid measurements. We found that the universal order parameter was able to capture more details of the grid models, especially in cases of decreasing moment of inertia. The most heterogeneous models showed very low synchronization and thus suggest a limitation of the second-order Kuramoto equation. Finally, we show local frequency results related to the multi-peaks of static models, which implies that spatial heterogeneity can also induce such multi-peak behavior., Comment: 7 pages, 7 figures

A new thermodynamic limit for the open circuit voltage of solar cells that includes thermalization is obtained in terms of photon entropy. A simple graphical construction makes it possible to link this limit to the existing limits for single junction cells due to Trivich and Flinn, Shockley and Queisser and W\"urfel, and the thermodynamic Carnot-type limit for hot-carrier solar cell. At the fundamental level, this limit points to similarity between photovoltaic and thermoelectric energy conversion.

We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new stationary state. Our study calculates displacement moments in discrete time (number of steps $N$) for an arbitrarily strong constant driving force, exact to first order in obstacle density. We find that for fixed driving force $F$, the approach to the terminal discrete velocity scales as $\sim N^{-1} \exp(- N F^2 / 16)$ for small $F$, differing significantly from the $\sim N^{-1}$ prediction of linear response. Besides a non-analytic dependence on the force and breakdown of Einstein's linear response, our results show that fluctuations in the directions of the force are enhanced in the presence of obstacles. Notably, the variance grows as $\sim N^3$ (superdiffusion) for $F \to \infty$ at intermediate steps, reverting to normal diffusion ($\sim N$) at larger steps, a behavior previously observed in continuous time but demonstrated here in discrete steps for the first time. Unlike the exponential waiting time case, the superdiffusion regime starts immediately at $N=1$. The framework presented allows considering any type of waiting-time distribution between steps and transition to continuous time using subordination methods. Our findings are also validated through computer simulations., Comment: 16 pages, 8 figures

Cargo distribution within eukaryotic cells relies on the active transport mechanisms driven by molecular motors. Despite their critical role, the intricate relationship between motor transport properties and cargo binding - and its impact on motor distribution - remains inadequately understood. Additionally, improper regulation of ubiquitination, a pivotal post-translational modification that affects protein degradation, activation, and localization, is associated with several neurodegenerative diseases. Recent data showed that ubiquitination can alter motor-cargo binding of the Kinesin-3 motor UNC-104 / KIF1A that transports synaptic vesicles. To investigate how ubiquitin-like modifications affect motor protein function, particularly cargo binding, transport properties, and distribution, we utilize the PLM neuron of C. elegans as a model system. Using fluorescent microscopy, we assess the distribution of cargo-bound UNC-104 motors along the axon and probe their dynamics using FRAP experiments. We model cargo binding kinetics with a Master equation and motor density dynamics using a Fokker-Planck approach. Our combined experimental and theoretical analysis reveals that ubiquitin-like knockdowns enhance UNC-104's cooperative binding to its cargo. However, these modifications do not affect UNC-104's transport properties, such as processivity and diffusivity. Thus, while ubiquitin-like modifications significantly impact the cargo-binding of UNC-104, they do not alter its transport dynamics, keeping the homeostatic distribution of UNC-104 unchanged., Comment: 13 pages, 8 figures

We propose a simple model of an interacting, fully spin--polarized Fermi gas in dimensions $d=2$ and $d=3$, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first--order phase transitions between the low and high density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for $d=2$ and $3$, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embeded in the fermionic nature of the system under study., Comment: 10 pages, 11 figures

Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent advances in experimental techniques for controlling and preparing these systems have increased interest in this area, as they have the potential to drive the development of quantum technologies. In this study, we present a density-functional theory approach to extract detailed information about the statistics of work and the irreversible entropy associated with quantum quenches at finite temperature. Specifically, we demonstrate that these quantities can be expressed as functionals of thermal and out-of-equilibrium densities, which may serve as fundamental variables for understanding finite-temperature many-body processes. We, then, apply our method to the case of the inhomogeneous Hubbard model, showing that our density functional theory based approach can be usefully employed to unveil the distinctive roles of interaction and external potential on the thermodynamic properties of such a system.

We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the finite sampling cannot cover the whole configuration space. As a proof of concept, the estimator is applied to calculate the partition function for several model systems, and the results are compared with the numerically exact solutions. Excellent agreement is found, demonstrating that a solution for an efficient calculation of partition functions is possible.

Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various relationships with wide research areas such as the coupled limit-cycle oscillators, the dislocation theory, a block-spring model of earthquakes, and the nonequilibrium molecular dynamics. We show numerically several unique nonequilibrium properties of the coupled oscillators. We find that the spatial profiles of the average value and variance of the velocity become non-uniform when the dissipation rate is large. The probability distribution of the velocity sometimes deviates from the Gaussian distribution. The time evolution of kinetic energy becomes intermittent when the shear rate is small and the temperature is small but not zero. The intermittent jumps of the kinetic energy cause a long tail in the velocity distribution., Comment: 9 pages, 12 figures

We derive the Fokker-Planck equation for an active particle with both radial and tangential force and perturbative force, and its approximate solution of joint probability density is obtained. In t>>u and u=0 regions, an active particle leads to a super-diffusive distribution for radial velocity, while the mean squared tangential velocity with both radial and tangential force and perturbative force behaviors the Gaussian diffusion. As a result, the joint probability density obtained may be similarly consistent with that for the self-propelled particle., Comment: 14 pages, 2 Tables

Partial solvability plays an important role in the context of statistical mechanics, since it has turned out to be closely related to the emergence of quantum many-body scar states, i.e., exceptional energy eigenstates which do not obey the strong version of the eigenstate themalization hypothesis. We show that partial solvability of a quantum many-body system can be maintained even when the system is coupled to boundary dissipators under certain conditions. We propose two mechanisms that support partially solvable structures in boundary dissipative systems: The first one is based on the restricted spectrum generating algebra, while the second one is based on the Hilbert space fragmentation. From these structures, we derive exact eigenmodes of the Gorini-Kossakowski-Sudarshan-Lindblad equation for a family of quantum spin chain models with boundary dissipators, where we find various intriguing phenomena arising from the partial solvability of the open quantum systems, including persistent oscillations (quantum synchronization) and the existence of the matrix product operator symmetry. We discuss how the presence of solvable eigenmodes affects long-time behaviors of observables in boundary dissipative spin chains based on numerical simulations using the quantum trajectory method., Comment: 30 pages, 7 figures, 2 tables

We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis we find that each problem exhibits highly complex novel scaling behavior, arising from the intrinsically indeterministic ('random') nature of quantum mechanical measurements, which is governed by a measurement-dominated RG fixed point that we study within an $\epsilon$ expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured groundstate, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (CFT); (iii): universal 'effective central charges' $c^{({\rm eff})}_n$ for the prefactors of the logarithm of subsystem size of the $n$th R\'enyi entropies, which are independent of each other for different $n$, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy' $S_{\rm{eff}}$ which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. - A subset of these results have so-far also been obtained within the $\epsilon$ expansion for the measurement-dominated critical point in the critical Ising case (b)., Comment: 37 pages, 4 figures, 1 table

In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially defined by a regular square lattice and with probability $p$ each site is tested for the possibility of creating a long-range interaction with any other site that has not yet received one. Here, we used the specific case where $p=1$, meaning that every site in the network has one long-range interaction in addition to the short-range interactions of the regular lattice. These long-range interactions depend on a power-law form, $J_{ij}=r_{ij}^{-\alpha}$, with the geometric distance $r_{ij}$ between connected sites $i$ and $j$. In current two-dimensional model, we found that mean-field critical behavior is observed only at $\alpha=0$. As $\alpha$ increases, the network size influences the phase transition point of the system, i.e., indicating a crossover behavior. However, given the two-dimensional system, we found the critical behavior of the short-range interaction at $\alpha\approx2$. Thus, the limitation in the number of long-range interactions compared to the globally coupled model, as well as the form of the decay of these interactions, prevented us from finding a regime with finite phase transition points and continuously varying critical exponents in $0<\alpha<2$., Comment: 7 pages, 8 figures, 2 tables

Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by earlier work such as flux-insertion arguments. It turns out that the ingappabilities of quantum discrete height model is protected by an exotic "modulating" translation symmetry, which is a combination of modulating internal symmetry transformation and the conventional lattice translation. It can be also generalize to higher-form gauge fields in arbitrary dimensions, e.g., $\mathbb{Z}$-gauge theory in two dimensions with $\mathbb{Z}$ one-form symmetry and a modulating translation symmetry.

We present a general framework to implement massive Nambu-Goldstone quasi-particles in driven many-body systems. The underlying mechanism leverages an explicit Lie group structure imprinted into an effective Hamiltonian that governs the dynamics of slow degrees of freedom; the resulting emergent continuous symmetry is weakly explicitly broken, giving rise to a massive Nambu-Goldstone mode, with a spectral mass gap scaling linearly with the drive period. We discuss explicit and experimentally implementable realizations, such as Heisenberg-like spin models that support gapped spin-wave excitations. We provide a protocol to certify the existence of the massive Nambu-Goldstone mode from the dynamics of specific observables, and analyse the dispersion spectrum and their lifetime in the presence of weak explicit symmetry breaking.

We consider quantum transport on a tight-binding model on the Bethe lattice of a finite generation, or the Cayley tree, which may model the energy transport in a light-harvesting molecule. As a new feature to analyze the quantum transport, we add complex potentials for sources on the peripheral sites and for a drain on the central site. We find that the eigenstates that can penetrate from the peripheral sites to the central site are quite limited to the number of generation. All the other eigenstates are localized around the peripheral sites and cannot reach the central site. The former eigenstates can carry the current, which reduces the problem to the quantum transport on a parity-time ($PT$)-symmetric tight-binding chain. When the number of links is common to all generations, the current takes the maximum value at the exceptional point for the zero-energy states, which emerges because of the non-Hermiticity due to the $PT$-symmetric complex potentials. As we introduce randomness in the number of links in each generation of the tree, the resulting linear chain is a random-hopping tight-binding model. We find that the current reaches its maximum not exactly but approximately for a zero-energy state, although it is no longer located at an exceptional point in general., Comment: 41 pages, 17 figures

We present a thorough investigation of non-stabilizerness - a fundamental quantum resource that quantifies state complexity within the framework of quantum computing - in a one-dimensional U(1) lattice gauge theory. We show how non-stabilizerness is always extensive with volume, and has no direct relation to the presence of critical points. However, its derivatives typically display discontinuities across the latter: This indicates that non-stabilizerness is strongly sensitive to criticality, but in a manner that is very different from entanglement (that, typically, is maximal at the critical point). Our results indicate that error-corrected simulations of lattice gauge theories close to the continuum limit have similar computational costs to those at finite correlation length and provide rigorous lower bounds for quantum resources of such quantum computations., Comment: 5 pages + supplement. Comments welcome!!

We revisit the problem of describing creep in heterogeneous materials by an effective temperature by considering more realistic (and complex) non-mean-field elastic redistribution kernels. We show first, from theoretical considerations, that, if elastic stress redistribution and memory effects are neglected, the average creep failure time follows an Arrhenius expression with an effective temperature explicitly increasing with the quenched heterogeneity. Using a thermally activated progressive damage model of compressive failure, we show that this holds true when taking into account elastic interactions and memory effects, however with an effective temperature $T_{eff}$ depending as well on the nature of the (non-democratic) elastic interaction kernel. We observe that the variability of creep lifetimes, for given external conditions of load and temperature, is roughly proportional to the mean lifetime, therefore depends as well on $T$, on quenched heterogeneity, and the elastic kernel. Finally, we discuss the implications of this effective temperature effect on the interpretation of macroscopic creep tests to estimate an activation volume at the microscale.

Fundamental Measure Theory (FMT) is a successful and versatile approach for describing the properties of the hard-sphere fluid and hard-sphere mixtures within the framework of classical density functional theory (DFT). Lutsko [Phys. Rev. E 102, 062137 (2020)] introduced a version of FMT containing two free parameters, to be fixed by additional physical constraints. Whereas Lutsko focused on the stability of crystalline phases, we introduce and employ two statistical mechanical sum rules pertinent for the fluid phase, that are not automatically satisfied by FMT. By minimizing the relative deviation between different routes to calculate the excess chemical potential and the isothermal compressibility we determine the two free parameters of the theory. Our results indicate that requiring consistency with these sum rules can improve the quality of predictions of FMT for properties of the hard-sphere fluid phase. We suggest that employing these (test particle) sum rules, which apply for any interparticle pair-potential, might provide a means of testing the performance and accuracy of general DFT approximations.

Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows the system with a partial `memory' of its prior conditions, but is imperfect on long time scales due to the development of a turbulent cascade to small scales, which breaks the precise conservation of phase volume, making this memory imprecise. The equilibria are still determined by the short-time collisionless invariants, but the invariants themselves are driven to a universal form by the nature of the turbulence. This is numerically confirmed for the case of beam instabilities in one-dimensional electrostatic plasmas, where sufficiently strong turbulence appears to cause the distribution function of particle energies to develop a universal power-law tail, with exponent -2., Comment: 11 pages, 7 figures

In this study, we propose a new method for constrained combinatorial optimization using tensor networks. Combinatorial optimization methods employing quantum gates, such as quantum approximate optimization algorithm, have been intensively investigated. However, their limitations in errors and the number of qubits prevent them from handling large-scale combinatorial optimization problems. Alternatively, attempts have been made to solve larger-scale problems using tensor networks that can approximately simulate quantum states. In recent years, tensor networks have been applied to constrained combinatorial optimization problems for practical applications. By preparing a specific tensor network to sample states that satisfy constraints, feasible solutions can be searched for without the method of penalty functions. Previous studies have been based on profound physics, such as U(1) gauge schemes and high-dimensional lattice models. In this study, we devise to design feasible tensor networks using elementary mathematics without such a specific knowledge. One approach is to construct tensor networks with nilpotent-matrix manipulation. The second is to algebraically determine tensor parameters. For the principle verification of the proposed method, we constructed a feasible tensor network for facility location problem and conducted imaginary time evolution. We found that feasible solutions were obtained during the evolution, ultimately leading to the optimal solution. The proposed method is expected to facilitate the discovery of feasible tensor networks for constrained combinatorial optimization problems., Comment: 21 pages, 9 figures

Information processing in networks entails a dynamical transfer of information between stochastic variables. Transfer entropy is widely used for quantification of the directional transfer of information between input and output trajectories. However, currently there is no exact technique to quantify transfer entropy given the dynamical model of a general network. Here we introduce an exact computational algorithm, Transfer Entropy-Path Weight Sampling (TE-PWS), to quantify transfer entropy and its variants in an arbitrary network in the presence of multiple hidden variables, nonlinearity, transient conditions, and feedback. TE-PWS extends a recently introduced algorithm Path Weight Sampling (PWS) and uses techniques from the statistical physics of polymers and trajectory sampling. We apply TE-PWS to linear and nonlinear systems to reveal how transfer entropy can overcome naive applications of data processing inequalities in presence of feedback., Comment: 12 pages, 4 figures

This work examines the full scope of long-standing conjectures identifying the invariant thermodynamic curvature $R$ as the correlation volume $\xi^d$ and also as a measure of underlying statistical interactions. To this end, we set up a two-parameter ANNNI (Axial Next Nearest Neighbour Ising) chain featuring two next nearest neighbour (nnn) and a nearest neighbour (nn) interaction. Competition between interactions and resulting frustration engender a rich phase behaviour including a cross-over between two ferrimagnetic sub-phases. We show that $R$ attests to all its conjectured attributes with valuable insights into the character of mesoscopic fluctuating substructures. In a remarkable demonstration of its relevance at a far-from-critical point, $R$ is shown to resolve a hitherto unnoticed tricky issue involving $\xi$. A physically transparent expression for the zero field $R$ helps bring into focus the pivotal role played by some third order fluctuation moments.

We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a coloured noise can lead to a Kapitza pendulum-like stabilization of an unstable configuration provided the noise is anti-correlated. Further, we show that for modulation by a white noise of amplitude $\lambda$ and correlation strength $F$, the system will have an extremely large response if the product of $\lambda^{2}F$ equals a specific combination of the frequency and the damping coefficient. This prediction can be experimentally tested., Comment: 18 pages, 5 figures

We derive a Fokker-Planck equation for joint probability density for an active particle coupled two heat reservoirs with harmonic, viscous, random forces. The approximate solution for the joint distribution density of all-to-all and three others topologies is solved, which apply an exponential correlated Gaussian force in three-time regions of correlation time. Mean squared displacement, velocity behaviors in the form of super-diffusion, while the mean squared displacement, velocity has the Gaussian form, normal diffusion. Concomitantly, the Kurtosis, correlation coefficient, and moment from moment equation are approximately and numerically calculated., Comment: 13 pages, 3 Tables

We firstly study the Navier-Stokes equation for the motion of a passive particle with harmonic, viscous, perturbative forces, subject to an exponentially correlated Gaussian force. Secondly, from the Fokker-Planck equation in an incompressible conducting fluid of magnetic field, we approximately obtain the solution of the joint probability density by using double Fourier transforms in three-time domains. In addition, the kurtosis, the correlation coefficient, and the moment from moment equation are numerically calculated., Comment: 19 pages, 5 Tables