Search

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Due to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization. Here we achieve this goal by realizing quantum critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time-evolution of the Schr\"odinger equation in small spin glasses. We then measure dynamics in 3D spin glasses on thousands of qubits, where simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for a scaling advantage in reducing energy as a function of annealing time.

We relax the strong rationality assumption for the agents in the paradigmatic Kyle model of price formation, thereby reconciling the framework of asymmetrically informed traders with the Adaptive Market Hypothesis, where agents use inductive rather than deductive reasoning. Building on these ideas, we propose a stylised model able to account parsimoniously for a rich phenomenology, ranging from excess volatility to volatility clustering. While characterising the excess-volatility dynamics, we provide a microfoundation for GARCH models. Volatility clustering is shown to be related to the self-excited dynamics induced by traders' behaviour, and does not rely on clustered fundamental innovations. Finally, we propose an extension to account for the fragile dynamics exhibited by real markets during flash crashes., Comment: 20 pages, 8 figures

Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equilibrium feedback-driven Ising like class of neural networks that simultaneously and quantitatively captures scale-free avalanches and scale-specific oscillations. In the most simple yet fully microscopic model version we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations and collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time bins. Importantly, the inferred parameters correlate with model-independent signatures of "closeness to criticality", indicating that the coexistence of scale-specific (neural oscillations) and scale-free (neuronal avalanches) dynamics in brain activity occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations., Comment: 29 pages, 20 figures

We consider the discrete defocusing nonlinear Schr\"odinger equation in its integrable version, which is called defocusing Ablowitz-Ladik lattice. We consider periodic boundary conditions with period $N$ and initial data sample according to the Generalized Gibbs ensemble. In this setting, the Lax matrix of the Ablowitz-Ladik lattice is a random CMV-periodic matrix and it is related to the Killip-Nenciu Circular $\beta$-ensemble at high-temperature. We obtain the generalized free energy of the Ablowitz-Ladik lattice and the density of states of the random Lax matrix by establishing a mapping to the one-dimensional log-gas. For the Gibbs measure related to the Hamiltonian of the Ablowitz-Ladik flow, we obtain the density of states via a particular solution of the double-confluent Heun equation., Comment: 33 pages, 1 figures. We corrected some typos, add some references and simplified some proofs

The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular dynamics and Monte Carlo simulations in the last century. Computer studies have greatly enhanced both experimental discoveries and theoretical developments and constitute an active and continually expanding research field. Our goal in this review is to provide a modern perspective on this area. We describe the need to go beyond canonical methods to attack a problem that is notoriously difficult in terms of time scales, length scales, and physical observables. We first summarise recent algorithmic developments to achieve enhanced sampling and faster equilibration using replica exchange methods, cluster and swap Monte Carlo algorithms, and other techniques. We then review some major recent advances afforded by these novel tools regarding the statistical mechanical description of the liquid-to-glass transition as well as the mechanical, vibrational and thermal properties of the glassy solid. We finally describe some important challenges for future research., 17 pages, 5 figures, to be published in Nature Reviews Physics

We consider the Random-Cluster model on $\mathbb{Z}^d$ with interactions of infinite range of the form $J_x = \psi(x)\mathsf{e}^{-\rho(x)}$ with $\rho$ a norm on $\mathbb{Z}^d$ and $\psi$ a subexponential correction. We first provide an optimal criterion ensuring the existence of a nontrivial saturation regime (that is, the existence of $\beta_{\rm sat}(s)>0$ such that the inverse correlation length in the direction $s$ is constant on $[0,\beta_{\rm sat}(s))$), thus removing a regularity assumption used in a previous work of ours. Then, under suitable assumptions, we derive sharp asymptotics (which are not of Ornstein-Zernike form) for the two-point function in the whole saturation regime $(0,\beta_{\rm sat}(s))$. We also obtain a number of additional results for this class of models, including sharpness of the phase transition, mixing above the critical temperature and the strict monotonicity of the inverse correlation length in $\beta$ in the regime $(\beta_{\rm sat}(s), \beta_{\rm c})$., Comment: Some changes in the presentation after revision. Version accepted for publication in Communications in Mathematical Physics

We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at special points, we obtain the eigenvalues and Bethe ansatz equations of the system. We also show that the method is universal and valid for the periodic boundary condition where the $U(1)$ symmetry is reserved. The results in this paper can be applied to studying the exact solution of the $A^{(2)}_n$-related integrable models with arbitrary $n$., Comment: 26 pages

We study the linear instabilities and bifurcations in the Selkov model for glycolysis with diffusion. We show that this model has a zero wave-vector, finite frequency Hopf bifurcation to a growing oscillatory but spatially homogeneous state and a saddle-node bifurcation to a growing inhomogeneous state with a steady pattern with a finite wavevector. We further demonstrate that by tuning the relative diffusivity of the two concentrations, it is possible to make both the instabilities to occur at the same point in the parameter space, leading to an unusual type of codimension-two bifurcation. We then show that in the vicinity of this bifurcation the initial conditions decide whether a spatially uniform oscillatory or a spatially periodic steady pattern emerges in the long time limit.

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

Solid-state ionic conduction is a key enabler of electrochemical energy storage and conversion. The mechanistic connections between material processing, defect chemistry, transport dynamics, and practical performance are of considerable importance, but remain incomplete. Here, inspired by studies of fluids and biophysical systems, we re-examine anomalous diffusion in the iconic two-dimensional fast-ion conductors, the $\beta$- and $\beta^{\prime\prime}$-aluminas. Using large-scale simulations, we reproduce the frequency dependence of alternating-current ionic conductivity data. We show how the distribution of charge-compensating defects, modulated by processing, drives static and dynamic disorder, which lead to persistent sub-diffusive ion transport at macroscopic timescales. We deconvolute the effects of repulsions between mobile ions, the attraction between the mobile ions and charge-compensating defects, and geometric crowding on ionic conductivity. Our quantitative framework based on these model solid electrolytes connects their atomistic defect chemistry to macroscopic performance with minimal assumptions and enables mechanism-driven 'atoms-to-device' optimization of fast-ion conductors., Comment: 45 pages, 23 figures. Additional code is available at https://github.com/apoletayev/anomalous_ion_conduction

The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum time-dependent density functional theory. This allows the theorems of density functional theory to relate non-relativistic quantum mechanics back to a classical statistical mechanical derivation of polymer self-consistent field theory for ring polymers in a 4 dimensional thermal-space. One dynamic postulate is added to two static postulates which allows for a complete description of quantum physics from a 5 dimensional thermal-space-time ensemble perspective which also removes the measurement problem. In the classical limit, a cylinder condition naturally arises as the thermal dimension becomes irrelevant, providing a justification for using 5 dimensions and a cylinder condition in general relativity, which is known to produce 4 dimensional space-time gravity and Maxwell's equations. Thus, in this approach, the postulates of electromagnetism become derived results of a special case of a ring polymer interpretation of quantum foundations., Comment: Under review since 26 Apr 2021 with Foundations of Physics

The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. One such material, graphene, is not only an excellent platform for the experimental realization of the hydrodynamic flow of electrons, but also allows for a controlled derivation of the hydrodynamic equations on the basis of kinetic theory. The resulting hydrodynamic theory of electronic transport in graphene yields quantitative predictions for experimentally relevant quantities, e.g. viscosity, electrical conductivity, etc. Here I review recent theoretical advances in the field, compare the hydrodynamic theory of charge carriers in graphene with relativistic hydrodynamics and recent experiments, and discuss applications of hydrodynamic approach to novel materials beyond graphene., Invited review for La Rivista del Nuovo Cimento published online as an Open Source paper. Automated arXiv formatting is somewhat incompatible with the Springer style file, specifically, some hyperlinks might be broken. For a properly formatted file please follow the DOI link

In this brief note, we demonstrate a generalised energy equipartition theorem for a generic electrical circuit with Johnson-Nyquist (thermal) noise. From quantum mechanical considerations, the thermal modes have an energy distribution dictated by Planck's law. For a resistive circuit with some inductance, it is shown that the real part of the admittance is proportional to a probability distribution function which modulates the contributions to the system's mean energy from various frequencies of the Fourier spectrum. Further, we analyse the case with a capacitor connected in series with an inductor and a resistor. The results resemble superstatistics, i.e. a superposition of two statistics and can be reformulated in the energy representation. The correct classical limit is obtained as $\hbar \rightarrow 0$., Comment: v2: Typos corrected

The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although also glasses are solids, their structure resembles closely the one of a liquid and hence the concept of structural defects becomes ill-defined. As a consequence it is very challenging to rationalize on a microscopic level the mechanical properties of glasses close to the yielding point and to relate plastic events to structural properties. Here we investigate the topological characteristics of the eigenvector field of the vibrational excitations of a two-dimensional glass model, notably the geometric arrangement of the topological defects as a function of vibrational frequency. We find that if the system is subjected to a quasistatic shear, the location of the resulting plastic events correlate strongly with the topological defects that have a negative charge. Our results provide thus a direct link between the structure of glasses prior their deformation and the plastic events during deformation.

We present a new description of the known large deviation function of the classical symmetric simple exclusion process by exploiting its connection with the quantum symmetric simple exclusion processes and using tools from free probability. This may seem paradoxal as free probability usually deals with non commutative probability while the simple exclusion process belongs to the realm of classical probability. On the way, we give a new formula for the free energy -- alias the logarithm of the Laplace transform of the probability distribution -- of correlated Bernoulli variables in terms of the set of their cumulants with non-coinciding indices. This latter result is obtained either by developing a combinatorial approach for cumulants of products of random variables or by borrowing techniques from Feynman graphs., 40 pages, submitted to the special issue of the Annales H. Poincare in memory of Krzysztof Gawedzki

We investigate defects in scalar field theories in four and six dimensions in a double-scaling (semiclassical) limit, where bulk loops are suppressed and quantum effects come from the defect coupling. We compute $\beta $-functions up to four loops and find that fixed points satisfy dimensional disentanglement -- i.e. their dependence on the space dimension is factorized from the coupling dependence -- and discuss some physical implications. We also give an alternative derivation of the $\beta$ functions by computing systematic logarithmic corrections to the Coulomb potential. In this natural scheme, $\beta $ functions turn out to be a gradient of a `Hamiltonian' function ${\cal H}$. We also obtain closed formulas for the dimension of scalar operators and show that instabilities do not occur for potentials bounded from below. The same formulas are reproduced using Rigid Holography., Comment: 35 pages, 1 figure; v3: published version

We present a translation of the 1933 paper by R. F\"urth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. This paper opened in some sense the way to the stochastic methods of quantization developed almost 30 years later by Edward Nelson and others., Comment: 23 pages, 4 figures

The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces -- domain walls between clusters of parallel spins. The Kramers--Wannier duality maps these surfaces into worldsheets of confining strings in the Wegner's ${\mathbb Z}_2$ gauge theory. We study the excitation spectrum of long Ising strings by simulating the ${\mathbb Z}_2$ gauge theory on a lattice. We observe a strong mixing between string excitations and the lightest glueball state and do not find indications for light massive resonances on the string worldsheet., 47 pages, 16 figures

We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space., Comment: 61 pages, 25 figures

Thanks to their prominent collective character, long-range interactions promote information spreading and generate forms of entanglement scaling, which cannot be observed in traditional systems with local interactions. In this work, we study the asymptotic behavior of the entanglement entropy for Kitaev chains with long-range hopping and pairing couplings decaying with a power law of the distance. We provide a fully-fledged analytical and numerical characterization of the asymptotic growth of the ground state entanglement in the large subsystem size limit, finding that the truly non-local nature of the model leads to an extremely rich phenomenology. Most significantly, in the strong long-range regime, we discovered that the system ground state may have a logarithmic, fractal, or volume-law entanglement scaling, depending on the value of the chemical potential and on the strength of the power law decay., Journal of High Energy Physics, 2023 (5), ISSN:1126-6708, ISSN:1029-8479

The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a randomly located target. There has been significant interest and controversy regarding optimal search strategies, especially for superdiffusive processes. The optimal search strategy is typically defined as the strategy that minimizes the time it takes a given single searcher to find a target, which is called a first hitting time (FHT). However, many systems involve multiple searchers and the important timescale is the time it takes the fastest searcher to find a target, which is called an extreme FHT. In this paper, we study extreme FHTs for any stochastic process that is a random time change of Brownian motion by a Levy subordinator. This class of stochastic processes includes superdiffusive Levy flights in any space dimension, which are processes described by a Fokker-Planck equation with a fractional Laplacian. We find the short-time distribution of a single FHT for any Levy subordinate Brownian motion and use this to find the full distribution and moments of extreme FHTs as the number of searchers grows. We illustrate these rigorous results in several examples and numerical simulations., 29 pages, 5 figures

We investigate the nonequilibrium critical behavior of the contact process with deterministic aperiodic temporal disorder implemented by choosing healing or infection rates according to a family of aperiodic sequences based on the quasiperiodic Fibonacci sequence. This family allows us to gauge the temporal fluctuations via a wandering exponent $\omega$ and put our work in the context of the Kinzel--Vojta--Dickman criterion for the relevance of temporal disorder to the critical behavior of nonequilibrium models. By means of analytic and numerical calculations, the generalized criterion is tested in the mean-field limit.

We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of interval collapse time, which we define as the time taken for a spatial interval, demarcated by a pair of Lagrangian tracers, to collapse at a shock. By calculating the dynamic scaling exponents of the moments of various orders of these interval collapse times, we show that (a) there is not one but an infinity of characteristic time scales and (b) the probability distribution function of the interval collapse times is non-Gaussian and has a power-law tail. Our study is based on (a) a theoretical framework that allows us to obtain dynamic-multiscaling exponents analytically, (b) extensive direct numerical simulations, and (c) a careful comparison of the results of (a) and (b). We discuss possible generalizations of our work to higher dimensions, for the stochastically forced Burgers equation, and to other compressible flows that exhibit turbulence with shocks.

The Ising chain with kinetic constraints provides many examples of totally irreversible zero-temperature dynamics leading to metastability with an exponentially large number of attractors. In most cases, the constrained zero-temperature dynamics can be mapped onto a model of random sequential adsorption. We provide a brief didactic review, based on the example of the constrained Glauber-Ising chain, of the exact results on the dynamics of these models and on their attractors that have been obtained by means of the above mapping. The Riviera model introduced recently by Puljiz et al. behaves similarly to the kinetically constrained Ising chains. This totally irreversible deposition model however does not enjoy the shielding property characterising models of random sequential adsorption. It can therefore neither be mapped onto such a model nor (in all likelihood) be solved by analytical means. We present a range of novel results on the attractors of the Riviera model, obtained by means of an exhaustive enumeration for smaller systems and of extensive simulations for larger ones, and put these results in perspective with the exact ones which are available for kinetically constrained Ising chains., 20 pages, 8 figures, 6 tables

Quantum metrology aims to use quantum resources to improve the precision of measurement. Quantum criticality has been presented as a novel and efficient resource. Generally, protocols of criticality-based quantum metrology often work without decoherence. In this paper, we address the issue whether the divergent feature of the inverted variance is indeed realizable in the presence of noise when approaching the QPT. Taking the quantum Rabi model (QRM) as an example, we obtain the analytical result for the inverted variance. We show that the inverted variance may be convergent in time due to the noise. When approaching the critical point, the maximum inverted variance demonstrates a power-law increase with the exponent -1.2, of which the absolute value is smaller than that for the noise-free case, i.e., 2. We also observe a power-law dependence of the maximum inverted variance on the relaxation rate and the temperature. Since the precision of the metrology is very sensitive to the noise, as a remedy, we propose performing the squeezing operation on the initial state to improve the precision under decoherence. In addition, we also investigate the criticality-based metrology under the influence of the two-photon relaxation. Contrary to the single-photon relaxation, the quantum dynamics of the inverted variance shows a completely-different behavior. It does not oscillate with the same frequency with respect to the re-scaled time for different dimensionless coupling strengths. Strikingly, although the maximum inverted variance still manifests a power-law dependence on the energy gap, the exponent is positive and depends on the dimensionless coupling strength. This observation implies that the criticality may not enhance but weaken the precision in the presence of two-photon relaxation. It can be well described by the non-linearity introduced by the two-photon relaxation., 6 pages, 5 figures

Symmetry and symmetry breaking are two pillars of modern quantum physics. Still, quantifying how much a symmetry is broken is an issue that has received little attention. In extended quantum systems, this problem is intrinsically bound to the subsystem of interest. Hence, in this work, we borrow methods from the theory of entanglement in many-body quantum systems to introduce a subsystem measure of symmetry breaking that we dub entanglement asymmetry. As a prototypical illustration, we study the entanglement asymmetry in a quantum quench of a spin chain in which an initially broken global $U(1)$ symmetry is restored dynamically. We adapt the quasiparticle picture for entanglement evolution to the analytic determination of the entanglement asymmetry. We find, expectedly, that larger is the subsystem, slower is the restoration, but also the counterintuitive result that more the symmetry is initially broken, faster it is restored, a sort of quantum Mpemba effect, a phenomenon that we show to occur in a large variety of systems., Comment: 7 pages, 5 figures. Text reorganized, new results for interacting integrable and non-integrable spin chains added. Final version published in Nature Communications

We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains, which provide constraints on finite-time fluctuations of time-additive quantities around their averages. We employ spectral, perturbation and martingale techniques, together with non-commutative $$L_2$$ L 2 theory, to derive: (i) a Bernstein-type concentration bound for time averages of the measurement outcomes of a quantum Markov chain, (ii) a Hoeffding-type concentration bound for the same process, (iii) a generalization of the Bernstein-type concentration bound for counting processes of continuous-time quantum Markov processes, (iv) new concentration bounds for empirical fluxes of classical Markov chains which broaden the range of applicability of the corresponding classical bounds beyond empirical averages. We also suggest potential application of our results to parameter estimation and consider extensions to reducible quantum channels, multi-time statistics and time-dependent measurements, and comment on the connection to so-called thermodynamic uncertainty relations.

We study phase transitions and critical phenomena in nonequilibrium steady states controlled by an electric field. We employ the D3/D7 model in the presence of a charge density and electric field at finite temperatures. The system undergoes the first-order and the second-order phase transitions under the variation of the electric field in the presence of dissipation. We numerically find that the critical exponents which we define for the nonequilibrium phase transition in this model take the mean-field values., 11 pages, 6 figures; v2:typos fixed, published in JHEP

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify., 38 pages, 7 figures

In this paper, we study the dynamics of end-of-the-world (EOW) branes in AdS with scalar fields localized on the branes as a new class of gravity duals of CFTs on manifolds with boundaries. This allows us to construct explicit solutions dual to boundary RG flows. We also obtain a variety of annulus-like or cone-like shaped EOW branes, which are not possible without the scalar field. We also present a gravity dual of a CFT on a strip with two different boundary conditions due to the scalar potential, where we find the confinement/deconfinement-like transition as a function of temperature and the scalar potential. Finally, we point out that this phase transition is closely related to the measurement-induced phase transition, via a Wick rotation., 54 pages + appendix, 34 figures, references added

The thermodynamic relations in the Tsallis statistics were studied with physical quantities. An additive entropic variable related to the Tsallis entropy was introduced by assuming the form of the first law of the thermodynamics. The fluctuations in the Tsallis statistics were derived with physical quantities with the help of the introduced entropic variable. It was shown that the mean squares of the fluctuations of the physical quantities in the Tsallis statistics are the same as those in the conventional statistics. The mean square of the fluctuation of the Tsallis entropy and the mean square of the fluctuation of the Tsallis temperature were also derived. The mean square of the relative fluctuation of the Tsallis entropy and the mean square of the relative fluctuation of the Tsallis temperature are represented with heat capacities. It was shown that these fluctuations of the Tsallis quantities have the $q$-dependent terms in the Tsallis statistics of the entropic parameter $q$., Comment: 10 pages

We study the operator growth in open quantum systems with dephasing dissipation terms, extending the Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on the study of the dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by the Markovian dynamics. We introduce a notion of ''operator size concentration'' which allows a diagrammatic and combinatorial proof of the asymptotic linear behavior of the two sets of Lanczos coefficients ($a_n$ and $b_n$) in the large $q$ limit. Our results corroborate with the semi-analytics in finite $q$ in the large $N$ limit, and the numerical Arnoldi iteration in finite $q$ and finite $N$ limit. As a result, Krylov complexity exhibits exponential growth following a saturation at a time that grows logarithmically with the inverse dissipation strength. The growth of complexity is suppressed compared to the closed system results, yet it upper bounds the growth of the normalized out-of-time-ordered correlator (OTOC). We provide a plausible explanation of the results from the dual gravitational side., v3: acknowledgment updated, published version in JHEP

Non-Gaussian noise influences many complex out-of-equilibrium systems on a wide range of scales such as quantum devices, active and living matter, and financial markets. Despite the ubiquitous nature of non-Gaussian noise, its effect on activated transitions between metastable states has so far not been understood in generality, notwithstanding prior work focusing on specific noise types and scaling regimes. Here, we present a unified framework for a general class of non-Gaussian noise, which we take as any finite-intensity noise with independent and stationary increments. Our framework identifies optimal escape paths as minima of a stochastic action, which enables us to derive analytical results for the dominant scaling of the escape rates in the weak-noise regime generalizing the conventional Arrhenius law. We show that non-Gaussian noise always induces a more efficient escape, by reducing the effective potential barrier compared to the Gaussian case with the same noise intensity. Surprisingly, for a broad class of amplitude distributions even noise of infinitesimally small intensity can induce an exponentially larger escape rate. As the underlying reason we identify the appearance of discontinuous minimal action paths, for which escape from the metastable state involves a finite jump. We confirm the existence of such paths by calculating the prefactor of the escape rate, as well as by numerical simulations. Our results highlight fundamental differences in the escape behaviour of systems subject to thermal and non-thermal fluctuations, which can be tuned to optimize switching behaviour in metastable systems.

In this note, we formulate and study a Hamilton-Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton-Jacobi theory consistently describes thermodynamic transformations on the space of externally controllable parameters or equivalently, the space of equilibrium states. It turns out that in the Hamilton-Jacobi description, the choice of the principal function is not unique but, the resultant dynamical description for a given transformation remains the same irrespective of this choice. Some examples involving thermodynamic transformations of the ideal gas are discussed where the characteristic curves on the space of equilibrium states completely describe the dynamics. The geometric Hamilton-Jacobi formulation which has emerged recently is also discussed in the context of thermodynamics., Comment: v1: Preliminary version; v2: Revised version; v3: Typos corrected

This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian action. This aim is attained for homogeneous systems, described by a finite number of state variables depending on time only. In particular, it is shown that away from equilibrium free energy and entropy are independent constitutive functions.

An equation of pair correlation function has been derived from the first two members of BBGKY hierarchy in a weakly coupled inhomogeneous self gravitating system in quasi thermal equilibrium. This work may be useful to study the thermodynamic properties of the central region of a star cluster which is older than a few or more central relaxation time.

International audience; Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible schemes. Efficient algorithms known as event-chain Monte Carlo were then developed to reach necessary accelerations. They are based on non-reversible continuoustime Markov processes. Proving invariance and ergodicity for such schemes cannot be done as for discrete-time schemes and a theoretical framework to do so was lacking, impeding the generalisation of ECMC algorithms to more sophisticated systems or processes. In this work, we characterize the Markov processes generated in ECMC as piecewise deterministic Markov processes. It first allows us to propose more general schemes, for instance regarding the direction refreshment. We then prove the invariance of the correct stationary distribution. Finally, we show the ergodicity of the processes in soft-and hard-sphere systems, with a density condition for the latter.

International audience; We complete the kinetic theory of two-dimensional (2D) point vortices initiated in previous works. We use a simpler and more physical formalism. We consider a system of 2D point vortices submitted to a small external stochastic perturbation and determine the response of the system to the perturbation. We derive the diffusion coefficient and the drift by polarization of a test vortex. We introduce a general Fokker-Planck equation involving a diffusion term and a drift term. When the drift by polarization can be neglected, we obtain a secular dressed diffusion (SDD) equation sourced by the external noise. When the external perturbation is created by a discrete collection of N point vortices, we obtain a Lenard-Balescu-like kinetic equation reducing to a Landau-like kinetic equation when collective effects are neglected. We consider a multi-species system of point vortices. We discuss the process of kinetic blocking in the single and multi-species cases. When the field vortices are at statistical equilibrium (thermal bath), we establish the proper expression of the fluctuation-dissipation theorem for 2D point vortices relating the power spectrum of the fluctuations to the response function of the system. In that case, the drift coefficient and the diffusion coefficient satisfy an Einstein-like relation and the Fokker Planck equation reduces to a Smoluchowski-like equation. We mention the analogy between 2D point vortices and stellar systems. In particular, the drift of a point vortex in 2D hydrodynamics is the counterpart of the Chandrasekhar dynamical friction in astrophysics. We also consider a gas of 2D Brownian point vortices described by N coupled stochastic Langevin equations and determine its mean and mesoscopic evolution. In the present paper, we treat the case of unidirectional flows but our results can be straightforwardly generalized to axisymmetric flows.

A pair of the 2D non-unitary minimal models $M(2,5)$ is known to be equivalent to a variant of the $M(3,10)$ minimal model. We discuss the RG flow from this model to another non-unitary minimal model, $M(3,8)$. This provides new evidence for its previously proposed Ginzburg-Landau description, which is a $\mathbb{Z}_2$ symmetric theory of two scalar fields with cubic interactions. We also point out that $M(3,8)$ is equivalent to the $(2,8)$ superconformal minimal model with the diagonal modular invariant. Using the 5-loop results for theories of scalar fields with cubic interactions, we exhibit the $6-\epsilon$ expansions of the dimensions of various operators. Their extrapolations are in quite good agreement with the exact results in 2D. We also use them to approximate the scaling dimensions in $d=3,4,5$ for the theories in the $M(3,8)$ universality class., Comment: 24 pages, 2 figures; v3: additional symmetry constraints pointed out, references added

We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors., Comment: 17 pages, 18 figures; v2: added Fig.10 on quantum scars, published version

Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has been to establish a true second law of entanglement, and in particular a unique function which governs all transformations between entangled systems, mirroring the role of entropy in thermodynamics. Contrary to previous promising evidence, here we show that this is impossible, and no direct counterpart to the second law of thermodynamics can be established. This is accomplished by demonstrating the irreversibility of entanglement theory from first principles -- assuming only the most general microscopic physical constraints of entanglement manipulation, we show that entanglement theory is irreversible under all non-entangling transformations. We furthermore rule out reversibility without significant entanglement expenditure, showing that reversible entanglement transformations require the generation of macroscopically large amounts of entanglement according to certain measures. Our results not only reveal fundamental differences between quantum entanglement transformations and thermodynamic processes, but also showcase a unique property of entanglement which distinguishes it from other known quantum resources., Comment: 21+36 pages, 3 figures. Final published version. v3: significant revisions of the presentation, many additional clarifications

We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive interactions is connected, we vary the interaction (denoted by $t$) at a fixed edge. It is already known that each zero is monotonic (either increasing or decreasing) in $t$; we prove that its motion is local: the entire trajectories of any two distinct zeros are disjoint. If the underlying graph is a complete graph and all interactions take the same value $t\geq 0$ (i.e., the Curie-Weiss model), we prove that all the principal zeros (those in $i[0,\pi/2)$) decrease strictly in $t$., Comment: 16 pages, 1 figure

Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin-Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati differential equations along the large deviation minimizers or instantons, either forward or backward in time. Previous works in this direction often rely on the existence of isolated minimizers with positive definite second variation. By adopting techniques from field theory and explicitly evaluating the large deviation prefactors as functional determinant ratios using Forman's theorem, we extend the approach to general systems where degenerate submanifolds of minimizers exist. The key technique for this is a boundary-type regularization of the second variation operator. This extension is particularly relevant if the system possesses continuous symmetries that are broken by the instantons. We find that removing the vanishing eigenvalues associated with the zero modes is possible within the Riccati formulation and amounts to modifying the initial or final conditions and evaluation of the Riccati matrices. We apply our results in multiple examples including a dynamical phase transition for the average surface height in short-time large deviations of the one-dimensional Kardar-Parisi-Zhang equation with flat initial profile., 46 pages, 7 figures

Acknowledgements: M. Bruna was supported by a Royal Society University Research Fellowship (grant no. URF/R1/180040). J. Mason was supported by the Royal Society Award (RGF/EA/181043) and the Cantab Capital Institute for the Mathematics of Information of the University of Cambridge. The authors thank Tal Agranov, Mike Cates and Jon Chapman for helpful discussions., Funder: Cantab Capital Institute for the Mathematics of Information of the University of Cambridge, We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of partial differential equations for the two species’ densities. First, our result captures non-trivial interaction terms neglected in the mean-field approach, including a non-diagonal mobility matrix with explicit density dependence. Second, it generalises the rigorous hydrodynamic limit of Quastel (Commun Pure Appl Math 45(6):623–679, 1992), valid for species with equal jump rates and given in terms of a non-explicit self-diffusion coefficient, to the case of unequal rates in the dilute regime. In the equal-rates case, by combining matched asymptotic approximations in the low- and high-density limits, we obtain a cubic polynomial approximation of the self-diffusion coefficient that is numerically accurate for all densities. This cubic approximation agrees extremely well with numerical simulations. It also coincides with the Taylor expansion up to the second-order in the density of the self-diffusion coefficient obtained using a rigorous recursive method.

Glass formation is encountered in diverse materials. Experiments have revealed that dynamic relaxation spectra of supercooled liquids generically become asymmetric near the glass transition temperature, $T_g$, where an extended power law emerges at high frequencies. The microscopic origin of this "wing" remains unknown, and was so far inaccessible to simulations. Here, we develop a novel computational approach and study the equilibrium dynamics of model supercooled liquids near $T_g$. We demonstrate the emergence of a power law wing in numerical spectra, which originates from relaxation at rare, localised regions over broadly-distributed timescales. We rationalise the asymmetric shape of relaxation spectra by constructing an empirical model associating heterogeneous activated dynamics with dynamic facilitation, which are the two minimal physical ingredients revealed by our simulations. Our work offers a glimpse of the molecular motion responsible for glass formation at relevant experimental conditions., Comment: 5 pages, 4 figures, supplementary materials

One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space-time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the $C^*$ algebra description of statistical mechanics by the Gelfand-Naimark-Segal construction. Using Araki's exponential clustering and the Lieb-Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states., Comment: v1: 64 pages. v2: 70 pages; results and proofs for quantum spin chains clarified

Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rimini-Weber (GRW) theory, continuous spontaneous localization (CSL) model, Di\'osi-Penrose model, and dissipative GRW model - in the Wigner framework. The resulting master equations are approximated by Fokker-Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert's suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed., Comment: 22 pages, 2 figures

Landau-Ginzburg $\phi^4$ field theory is usually applied to systems for understanding continuous phase transitions at critical points. Here we analyze the thermal field using a similar free energy description from a statistical field theory perspective, and study fluctuations in such a field with a particular focus on realizing the thermal Casimir effect. Initially, we qualitatively describe the emergence of the Casimir-like effect using mean-field approximation and further derive it using coarse-graining of perturbative renormalization procedure in the vicinity of Gaussian-fixed point. These results may lead to further the understanding of the Casimir effect from scalar fields without employing the concept of zero-point energy in a cosmological sense., Comment: 9 pages, Added more clarification and references in this version

In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinite system of stochastic ordinary differential equations with white noise in the right-hand side, which models the point heat source. On the base of the previous analytical unsteady analysis an analytical formula in continuum approximation is suggested, which allows one to describe a steady-state kinetic temperature distribution in the graphene lattice in continuum approximation. The obtained solution is in a good agreement with numerical results obtained for the discrete system everywhere excepting a neighbourhood of six singular rays with the origin at the heat source location. The continuum solution becomes singular at these rays, unlike the discrete one, which appears to be localized in a certain sense along the rays. The factors, which cause such a directional localization and the mismatch between the continuum and discrete solutions are discussed. We expect that the suggested formula is applicable for various damped polyatomic lattices where all particles have equal masses in the case of universal for all particles external viscosity., Comment: 24 pages, 9 figures

We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by an interval when the system is in the ground state, either on the line or on the circle, and in the thermal Gibbs state on the line. We find that the restriction of the corresponding inversion maps to a spatial slice is obtained also in the gauge/gravity correspondence through the geodesic bit threads in a constant time slice of the dual static asymptotically AdS background. For a CFT in the thermal state on the line, the modular conjugation suggests the occurrence of a second world which can be related through the geodesic bit threads to the horizon of the BTZ black brane background. An inversion map is constructed also for the massless Dirac fermion in the ground state and on the line bipartite by the union of two disjoint intervals., Comment: 49 pages, 15 figures