The problem considered here is motivated by a work by Nachtergaele and Yau where the Euler equations of fluid dynamics are derived from many-body quantum mechanics, see (Commun Math Phys 243(3):485–540, 2003). A crucial concept in their work is that of local quantum Gibbs states, which are quantum statistical equilibria with prescribed particle, current, and energy densities at each point of space

In this paper we study a family of nonlinear \(\sigma \)-models in which the target space is the super manifold \(\mathbb {H}^{2|2N}\). These models generalize Zirnbauer’s \(\mathbb {H}^{2|2}\) nonlinear \(\sigma \)-model (Zirnbauer in Commun Math Phys 141(3):503–522, 1991). The latter model has a number of special features which aid in its analysis: through a remarkable technique from symplectic geometry

In this study, we investigate the metastable behavior of Metropolis-type Glauber dynamics associated with the Blume–Capel model with zero chemical potential and zero external field at very low temperatures. The corresponding analyses for the same model with zero chemical potential and positive small external field were performed in Cirillo and Nardi (J Stat Phys 150:1080–1114, 2013) and Landim and

We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature asymptotic limit. Our analysis concerns the multi-spin system that has q stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and

Heat engines are fundamental physical objects to develop the nonequilibrium thermodynamics. The thermodynamic performance of the heat engine is determined by the choice of cycle and time-dependence of parameters. Here, we propose a systematic numerical method to find a heat engine cycle to optimize some target functions. We apply the method to heat engines with slowly varying parameters and show that

We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic

This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein–Uhlenbeck systems \((X^\varepsilon _t(x))_{t\geqslant 0}\) with \(\varepsilon \)-small additive Lévy noise and initial value x. The driving noise processes include Brownian motion, \(\alpha \)-stable Lévy flights, finite intensity compound Poisson processes, and red noises, and may

The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles’ velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary

This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomous vector field whose flow exhibits an attracting heteroclinic network made by two 1-dimensional connections and a 2-dimensional separatrix between two equilibria with different Morse indices. After changing the parameters

We study the boundary value problem of two stationary BGK-type models—the BGK model for fast chemical reaction and the BGK model for slow chemical reaction—and provide a unified argument to establish the existence and uniqueness of stationary flows of reactive BGK models in a slab. For both models, the main difficulty arise in the uniform control of the auxiliary parameters from above and below, since

We present a hydrodynamical model for graphene nanoribbons that takes into account the electron collisions with the lattice and with the edge of the ribbon. Moreover the bandgap due to the low dimension of the ribbon is considered. The simulation shows that the model describes qualitatively the macroscopic behavior of the charges and the results are comparable with that ones obtained by solving numerically

We derive the Thouless–Anderson–Palmer (TAP) equations for the Ghatak and Sherrington model (J Phys C 10(16):3149–3156, 1977). Our derivation, based on the cavity method, holds at high temperature and at all values of the crystal field. It confirms the prediction of Yokota (J Phys Condens Matter 4(10):2615–2622, 1992).

This work considers an expansion of a dense monolayer of cells: a collective multicellular phenomenon, where cells divide, grow, and maintain contacts with their neighbors. During migration, cells display complex behavior, adjusting both their division rate and their growth after division to the local mechanical environment. Experimental observations show that cells near the edge of the expanding monolayer

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting is indeed possible, thus allowing a comparison. Moreover

We present a first-order aggregation model for a homogeneous Lohe matrix ensemble with higher order couplings via a gradient flow approach. For homogeneous free flow with the same Hamiltonian, it is well known that the Lohe matrix model with cubic couplings can be recast as a gradient system with a potential which is a squared Frobenius norm of of averaged state. In this paper, we further derive a

The paper treats an agent-based model with averaging dynamics to which we refer as the K-averaging model. Broadly speaking, our model can be added to the growing list of dynamics exhibiting self-organization such as the well-known Vicsek-type models (Aldana et al. in: Phys Rev Lett 98(9):095702, 2007; Aldana and Huepe in: J Stat Phys 112(1–2):135–153, 2003; Pimentel in: Phys. Rev. E 77(6):061138, 2008)

Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal the martingale structure for a general thermodynamic functional of inhomogeneous singularly perturbed diffusion processes under second-order averaging, where a general thermodynamic functional is defined as the logarithmic Radon–Nykodim

We study the macroscopic transport properties of the quantum Lorentz gas in a crystal with short-range potentials, and show that in the Boltzmann–Grad limit the quantum dynamics converges to a random flight process which is not compatible with the linear Boltzmann equation. Our derivation relies on a hypothesis concerning the statistical distribution of lattice points in thin domains, which is closely

We consider the Curie–Weiss Potts model in zero external field under independent symmetric spin-flip dynamics. We investigate dynamical Gibbs–non-Gibbs transitions for a range of initial inverse temperatures \(\beta <3\), which covers the phase transition point \(\beta = 4\log 2\) (Ellis and Wang in Stoch Process Appl 35(1):59–79, 1990). We show that finitely many types of trajectories of bad empirical

We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of fermions into the different reservoirs, as well as the mean entropy production rate of the dynamics. Formulas are explicitly expanded to leading

We consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state

We introduce a stochastic eight-vertex model motivated by the eight-vertex model in statistical mechanics. We study its invariant measures under a certain balance condition for the creation and annihilation probabilities of particles. We also discuss its scaling limits, that is, the hydrodynamic limit, and the linear and nonlinear fluctuations rather formally. We especially obtain a new type of KPZ-Burgers

We consider the bipartite Sherrington–Kirkpatrick model in which the variance of disorders depends only on the species the particles belong to. By using the stochastic calculus method, we obtain the fluctuation result for the partition function in the absence of an external field. When the external field is nonzero, the central limit theorem for the free energy is also derived through a different stochastic

We introduce a Kac’s type walk whose rate of binary collisions preserves the total momentum but not the kinetic energy. In the limit of large number of particles we describe the dynamics in terms of empirical measure and flow, proving the corresponding large deviation principle. The associated rate function has an explicit expression. As a byproduct of this analysis, we provide a gradient flow formulation

We study the numerical simulation of the shaken dynamics, a parallel Markovian dynamics for spin systems with local interaction and transition probabilities depending on the two parameters q and J that “tune” the geometry of the underlying lattice. The analysis of the mixing time of the Markov chain and the evaluation of the spin-spin correlations as functions of q and J, make it possible to determine

We consider the problem of metastability for stochastic dynamics with exponentially small transition probabilities in the low temperature limit. We generalize previous model-independent results in several directions. First, we give an estimate of the mixing time of the dynamics in terms of the maximal stability level. Second, assuming the dynamics is reversible, we give an estimate of the associated

In this paper we investigate the two-dimensional Abelian sandpile model in which the conservation of sand grains is locally violated using non-conservative lattice sites. We use spatially correlated arbitrary fractal patterns to mark the non-conservative sites. We have observed a “crossover” in the scaling behavior of the distribution functions of both the avalanche areas and avalanche sizes. The pre-crossover

We consider spin-flip dynamics of Ising lattice spin systems and study the time evolution of concentration inequalities. For “weakly interacting” dynamics we show that the Gaussian concentration bound is conserved in the course of time and it is satisfied by the unique stationary Gibbs measure. Next we show that, for a general class of translation-invariant spin-flip dynamics, it is impossible to evolve

We prove a quenched invariance principle for a class of random walks in random environment on \({\mathbb {Z}}^d\), where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the edge e at its current location to a new random edge \(e'\) (whose law depends on e) and then steps to the other endpoint of \(e'\). We show that a native environment

This paper is devoted to the linearized Vlasov–Poisson–Fokker–Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case

We study the radial distribution of pressure, density, temperature and flow velocity fields at different times in a two dimensional hard sphere gas that is initially at rest and disturbed by injecting kinetic energy in a localized region through large scale event driven molecular dynamics simulations. For large times, the growth of these distributions are scale invariant. The hydrodynamic description

We consider self-propelled particles confined between two parallel plates, moving with a constant velocity while their moving direction changes by rotational diffusion. The probability distribution of such micro-organisms in confined environment is singular because particles accumulate at the boundaries. This leads us to distinguish between the probability distribution densities in the bulk and in

We consider the preferential attachment model with location-based choice introduced by Haslegrave et al. (Random Struct Algorithms 56(3):775–795, 2020) as a model in which condensation phenomena can occur. In this model, each vertex carries an independent and uniformly distributed location. Starting from an initial tree, the model evolves in discrete time. At every time step, a new vertex is added

We study N vicious Brownian bridges propagating from an initial configuration \(\{a_1< a_2< \ldots < a_N \}\) at time \(t=0\) to a final configuration \(\{b_1< b_2< \ldots < b_N \}\) at time \(t=t_f\), while staying non-intersecting for all \(0\le t \le t_f\). We first show that this problem can be mapped to a non-intersecting Dyson’s Brownian bridges with Dyson index \(\beta =2\). For the latter we

In this paper we focus on strong solutions of some heat-like problems with a non-local derivative in time induced by a Bernstein function and an elliptic operator given by the generator or the Fokker–Planck operator of a Pearson diffusion, covering a large class of important stochastic processes. Such kind of time-non-local equations naturally arise in the treatment of particle motion in heterogeneous

The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important in applications. Despite this, while there has been much attention given to existence and stability of fully phase-locked states in the finite N Kuramoto model,

In this paper we consider a stochastic system with two connected nodes, whose unidirectional connection is variable and depends on point processes associated to each node. The input node is represented by an homogeneous Poisson process, whereas the output node jumps with an intensity that depends on the jumps of the input nodes and the connection intensity. We study a scaling regime when the rate of

A time-inhomogeneous Feller-type diffusion process with linear infinitesimal drift \(\alpha (t)x+\beta (t)\) and linear infinitesimal variance 2r(t)x is considered. For this process, the transition density in the presence of an absorbing boundary in the zero-state and the first-passage time density through the zero-state are obtained. Special attention is dedicated to the proportional case, in which

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large

A correction to this paper has been published: https://doi.org/10.1007/s10955-021-02770-w

We consider a homogeneous plasma composed of N particles of the same electric charge which interact through a Coulomb potential. In the large plasma parameter limit, classical kinetic theories justify that the empirical density is the solution of the Balescu–Guernsey–Lenard equation, at leading order. This is a law of large numbers. The Balescu–Guernsey–Lenard equation is approximated by the Landau

We provide here an explicit example of Khinchin’s idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics, as it is basically a matter of choosing the “proper” observables. This point of view is supported by extensive numerical simulation of the one-dimensional Toda chain, an integrable non-linear Hamiltonian system where

We study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky

We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations

We consider systems of N bosons trapped on the two-dimensional unit torus, in the Gross-Pitaevskii regime, where the scattering length of the repulsive interaction is exponentially small in the number of particles. We show that low-energy states exhibit complete Bose–Einstein condensation, with almost optimal bounds on the number of orthogonal excitations.

We consider the half-line stochastic heat equation (SHE) with Robin boundary parameter \(A = -\frac{1}{2}\). Under narrow wedge initial condition, we compute every positive (including non-integer) Lyapunov exponents of the half-line SHE. As a consequence, we prove a large deviation principle for the upper tail of the half-line KPZ equation under Neumann boundary parameter \(A = -\frac{1}{2}\) with

We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for \(p=\frac{1}{2}\) and \(p=\frac{3}{2}\). In those new cases one finds contributions from the Ramond sector, which were not present for positive integer p. The existence

We present a new dynamical proof of the Thouless–Anderson–Palmer (TAP) equations for the classical Sherrington–Kirkpatrick spin glass at sufficiently high temperature. In our derivation, the TAP equations are a simple consequence of the decay of the two point correlation functions. The methods can also be used to establish the decay of higher order correlation functions. We illustrate this by proving

We consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold \(\Omega \) of unit area. It is known that the average cost scales as \(E_{\Omega }(N)\sim {1}/{2\pi }\ln N\) with a correction that is at most of order \(\sqrt{\ln N\ln \ln N}\). In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the

The structure function of a random matrix ensemble can be specified in terms of the covariance of the linear statistics \(\sum _{j=1}^N e^{i k_1 \lambda _j}\), \(\sum _{j=1}^N e^{-i k_2 \lambda _j}\) for Hermitian matrices, and the same with the eigenvalues \(\lambda _j\) replaced by the eigenangles \(\theta _j\) for unitary matrices. As such it can be written in terms of the Fourier transform of the

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically

We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We compute the limiting values and fluctuations of the free energy as well as three types of overlaps in the setting where the strength of the external field goes

We consider stochastic growth models to represent population dynamics subject to geometric catastrophes. We analyze different dispersion schemes after catastrophes, to study how these schemes impact the population viability and comparing them with the scheme where there is no dispersion. In the schemes with dispersion, we consider that each colony, after the catastrophe event, has d new positions to

This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space \(C ^{1+Lip}\) symmetric bimodal maps. Moreover, we show that the topological entropy of the renormalization operator defined on the space of \(C^{1+Lip}\) symmetric bimodal maps is infinite. Further we prove the existence of a continuum of

We consider Kac’s 1D N-particle system coupled to an ideal thermostat at a fixed temperature, introduced by Bonetto, Loss, and Vaidyanathan in 2014. We obtain a propagation of chaos result for this system, with an explicit and uniform-in-time rate of order \(N^{-1/3}\) in terms of the 2-Wasserstein metric squared. We also show well-posedness and equilibration for the limit kinetic equation in the space

The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang in (J Stat Phys 165:866–906, 2016), to the inelastic Boltzmann equation with moderately soft potentials, which is also an extensive work of our preceding result in the inelastic Maxwellian molecules case. We first prove the existence and uniqueness

We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter \(\varepsilon \) such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with ergodic invariant measure. Convergence of the slow process to the solution of a homogenized stochastic differential equation (SDE) in the limit \(\varepsilon

We consider the process of opinion formation, in a society where there is a set of rules B that indicates whether a social instance is acceptable. Public opinion is formed by the integration of the voters’ attitudes which can be either conservative (mostly in agreement with B) or liberal (mostly in disagreement with B and in agreement with peer voters). These attitudes are represented by stable fixed