Journal of Statistical Physics最新文献

This paper addresses large-data local existence and uniqueness of classical solutions to the inhomogeneous Landau equation in the hard potentials case (including Maxwell molecules). Solutions have previously been constructed by Chaturvedi [SIAM J. Math. Anal., 55(5), 5345–5385, 2023] for initial data in an exponentially-weighted (H^{10}) space, but it is not a priori clear whether these solutions have more regularity than the initial data. We improve Chaturvedi’s existence result in two ways: our solutions are (C^infty ) for positive times, and we allow initial data in a sub-exponentially-weighted (L^infty ) space, at the cost of requiring a mild positivity condition at time zero. To prove uniqueness, we require stronger assumptions on the initial data: Hölder continuity and the absence of vacuum regions. These are the same assumptions that are required for uniqueness in prior work on the soft potentials case. Along the way to proving existence and uniqueness, we establish some useful results that were previously only known in the case of soft potentials, including spreading of positivity and propagation of Hölder continuity. Many of the proof strategies from the soft potentials case do not apply here because of the more severe loss of velocity moments.

In recent experiments, ants were constrained to a two-dimensional rectangular domain by enclosing them between two flat transparent surfaces and their dynamic behavior was studied. The large sides of the domain were in the vertical direction and thus, gravity affected the dynamics of the ants. The experiments showed that the collective dynamics of the ants displayed wave-like behavior. In this article, we develop and analyze a mathematical model of the mentioned experiments. Our work contributes to the understanding of the dynamics of active matter and its mathematical modeling.

The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this process relies on Perron-Frobenius theory for adjacency matrices. Generalizing to infinite graphs is rather delicate, and in this article, we study in detail specific models of the MERW on (mathbb {Z}) with loops, for both random and non-random loops. Thanks to an explicit combinatorial representation of the corresponding Perron-Frobenius eigenvectors, we are able to precisely determine the asymptotic behavior of these walks. We show, in particular, that essentially all MERWs on (mathbb {Z}) with loops have positive speed.

The dice lattice is a two-dimensional structure derived from hexagonal and triangular lattices, distinguished by its high degree of symmetry and distinctive physical properties. It holds significant relevance in the fields of mathematics, physics, and materials science, particularly in the investigation of topological phenomena and the dynamic behavior of low-dimensional systems. For a given graph G, let A(G), D(G), and Q(G) represent the adjacency matrix, degree matrix, and signless Laplacian matrix of G, respectively. We define

In this paper, we determine the (A_{alpha })-spectrum and (A_{alpha })-energy of the dice lattice under toroidal boundary conditions. Furthermore, we utilize these findings to derive the A-spectrum, Q-spectrum, A-energy, and Q-energy of the dice lattice with the same boundary conditions.

Consensus behavior is a notable emergence phenomenon in nature. It is only recently that consensus behavior has been demonstrated in the Vlasov alignment and Euler alignment models with low-order power-law potentials, i.e. (U(r)=r^{alpha }, alpha in [1,4)). Note that the attraction between particles weakens as (alpha ) grows, so it is interesting to consider the high-order power-law potential case. By some macroscopic and microscopic Lyapunov functionals, for any (alpha in (2,infty )) and any long range communication weight, we establish both the weak and strong consensus and their precise convergence rates for the Vlasov alignment and Euler alignment models.

We introduce a periodic extension of the Kingman model [11] for the balance between selection and mutation in large populations. In its original form, the model describes a population’s fitness distribution by a probability measure on the unit interval evolving through a simple discrete-time dynamical system, in which selection operates via size-biasing, and the mutation distribution remains constant along time. We allow the mutation environment to vary periodically over time and prove the convergence of the fitness distribution along subsequences; crucially, we derive an explicit criterion, phrased in term of the Perron eigenvalue of a characteristic matrix, to determine whether an atom emerges at the largest fitness in the limit, a phenomenon called condensation. Our results provide new insights on the role of periodic mutation effects in population Darwinian evolution.

Quantum systems in thermal equilibrium are described using Gibbs states. The correlations in such states determine how difficult it is to describe or simulate them. In this article, we show that if the Gibbs state of a quantum system satisfies that each of its marginals admits a local effective Hamiltonian with short-range interactions, then it satisfies a mixing condition, that is, for any regions A, C the distance of the reduced state (rho _{AC}) on these regions to the product of its marginals, ( left| rho _{AC} rho _A^{-1} otimes rho _C^{-1} - mathbbm {1}_{AC} right| , , ) decays exponentially with the distance between regions A and C. This mixing condition is stronger than other commonly studied measures of correlation. In particular, it implies the exponential decay of the mutual information between distant regions. The mixing condition has been used, for example, to prove positive log-Sobolev constants. On the way, we prove that the the condition regarding local effective Hamiltonian is satisfied if the Hamiltonian only has commuting interactions which also commute with every marginal of their products. The proof of these results employs a variety of tools such as Araki’s expansionals, quantum belief propagation and cluster expansions.

In this work we investigate spectral properties of squared random matrices with independent entries that have only two finite moments. We revisit the problem of perturbing a large, i.i.d. random matrix by a finite rank error. We prove that under a merely second moment condition, for a large class of perturbation matrix with bounded rank and bounded operator norm, the outlier eigenvalues of perturbed matrix still converge to that of the perturbation, which was previously known when matrix entries have finite fourth moment. We then show that the same perturbation holds for very sparse random matrices with i.i.d. entries, all the way up to a constant number of nonzero entries per row and column.

In this paper we introduce, inspired by Clausius and developing the ideas of [11], the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory. Besides providing a new proof of a formula derived in [3, 4], which is the basis of the equivalence, we show that equivalent quasistatic transformations can be distinguished in finite terms, by the renormalized work introduced in [1,2,3,4]. This allows us to tackle the problem of determining the optimal quasistatic transformation among the equivalent ones.

Recently, the concept of minimal dissipation has been brought forward as a means to define work performed on open quantum systems [Phys. Rev. A 105, 052216 (2022)]. We discuss this concept from the point of view of projection operator formalisms in classical statistical physics. We analyse an autonomous composite system which consists of a system and an environment in the most general sense (i.e. we neither impose conditions on the coupling between system and environment nor on the properties of the environment). One condition any useful definition of work needs to fulfil is that it reproduces the thermodynamic notion of work in the limit of weak coupling to an environment that has infinite heat capacity. We propose a projection operator route to a definition of work that reaches this limit and we discuss its relation to minimal dissipation.