Journal of Statistical Physics最新文献

We study a rumour propagation model along the lines of Lebensztayn and Rodriguez (Stat Probab Lett 78(14):2130–2136, 2008) as a long-range percolation model on (mathbb {Z}). We begin by showing a sharp phase transition-type behaviour in the sense of exponential decay of the survival time of the rumour cluster in the sub-critical phase. In the super-critical phase, under the assumption that radius of influence r.v. has (2+epsilon ) moment finite (for some (epsilon >0)), we show that the rightmost vertex in the rumour cluster has a deterministic speed in the sense that after appropriate scaling, the location of the rightmost vertex converges a.s. to a deterministic positive constant. Under the assumption that radius of influence r.v. has (4+epsilon ) moment finite, we obtain a central limit theorem for appropriately scaled and centered rightmost vertex. Later, we introduce a rumour propagation model with reactivation. For this section, we work with a family of exponentially decaying i.i.d. radius of influence r.v.’s, and we obtain the speed result for the scaled rightmost position of the rumour cluster. Each of these results is novel, in the sense that such properties have never been established before in the context of the rumour propagation model on (mathbb {Z}), to the best of our knowledge.

Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.

The problem of displacive phase transitions (by which crystals pass on heating from a less symmetric to a more symmetric form) is investigated through numerical integration of the Newton equations of motion for a realistic model, in the paradigmatic case of quartz. Usually such transitions are discussed in terms of the positions of the atoms, while the role of normal modes is emphasized here. The key preliminary property established, in agreement with the indications given by Landau in his thermodynamic-like approach, is that four well definite modes are sufficient to describe the transition, the remaining modes just acting as a noise. The main result is then that such four modes constitute a closed Hamiltonian subsystem presenting an effective potential parametrically dependent on specific energy. The effective potential is actually computed, through (appropriately defined) time-averages of the accelerations of the relevant modes, and is found to describe, as energy is varied, a pitchfork bifurcation, once more confirming in dynamical terms the Landau result. The effective potential also allows one to advance a possible explanation of the “soft mode” phenomenon, namely the occuring, in the Raman spectrum, of a peak whose frequency depends on temperature and vanishes at the transition.

Based on the theory of Carathéodory structure, this paper introduces several definitions of entropies for impulsive semi-flows on arbitrary subsets. We compare these definitions and establish relations of these definitions. We show an inverse variational principle between topological (tau )-entropy and measure theoretic (tau )-entropy. Moreover, a variational principle of packing (tau ) entropy of impulsive semi-flows is established.

It is generally believed (but not yet proved) that Ising spin glasses with nearest-neighbor interactions have a phase transition in three and higher dimensions to a low-temperature spin glass phase, but the nature of this phase remains controversial, especially whether it is characterized by multiple incongruent Gibbs states. Of particular relevance to this question is the behavior of the typical free energy difference restricted to a finite volume between two such putative Gibbs states, as well as the nature of the fluctuations of their free energy difference as the couplings within the volume vary. In this paper we investigate these free energy difference fluctuations by introducing a new kind of metastate which classifies Gibbs states through their edge overlap values with a reference Gibbs state randomly chosen from the support of the periodic boundary condition (PBC) metastate. We find that the free energy difference between any two incongruent pure states, regardless of the details of how they’re organized into mixed states within the PBC metastate, converges to a Gaussian (or Gaussian-like) distribution whose variance scales with the volume, proving a decades-old conjecture of Fisher and Huse. The same conclusion applies, though with some additional restrictions, to both mixed Gibbs states and ground states. We discuss some implications of these results.

The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is seen as a particular instance of an Ising model with a slowly varying magnetic field in the fixed magnetization ensemble. We first characterize the typical magnetization profiles in the regime in which the contribution of the magnetic field competes with the bulk energy term. We then discuss in more detail the particular case of a gravitational field and the arising interfacial phenomena. In particular, we identify the macroscopic profile and propose several conjectures concerning the interface appearing in the phase coexistence regime. The latter are supported by explicit computations in an effective model. Finally, we state some conjectures concerning equilibrium crystal shapes in the presence of a gravitational field, when the latter contributes to the energy only to surface order.

In this paper, we show that the Gibbs measure of the stochastic hyperbolic sine-Gordon equation on the circle is the unique invariant measure for the Markov process. Moreover, the Markov transition probabilities converge exponentially fast to the unique invariant measure in a type of 1-Wasserstein distance. The main difficulty comes from the fact that the hyperbolic dynamics does not satisfy the strong Feller property even if sufficiently many directions in a phase space are forced by the space-time white noise forcing. We instead establish that solutions give rise to a Markov process whose transition semigroup satisfies the asymptotic strong Feller property and convergence to equilibrium in a type of Wasserstein distance.

We investigate heat transport through a one-dimensional open coupled scalar field theory, depicted as a network of harmonic oscillators connected to thermal baths at the boundaries. The non-Hermitian dynamical matrix of the network undergoes a stability-to-instability transition at the exceptional points as the coupling strength between the scalar fields increases. The open network in the unstable regime, marked by the emergence of inverted oscillator modes, does not acquire a steady state, and the heat conduction is then unbounded for general bath couplings. In this work, we engineer a unique bath coupling where a single bath is connected to two fields at each edge with the same strength. This configuration leads to a finite steady-state heat conduction in the network, even in the unstable regime. We also study general bath couplings, e.g., connecting two fields to two separate baths at each boundary, which shows an exciting signature of approaching the unstable regime for massive fields. We derive analytical expressions for high-temperature classical heat current through the network for different bath couplings at the edges and compare them. Furthermore, we determine the temperature dependence of low-temperature quantum heat current in different cases.

This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and investigates their underlying properties. Thereafter, we extend certain classical findings on correlation entropy and local correlation entropy to the realm of free semigroup actions. Finally, we establish the interconnections between topological entropy, measure-theoretic entropy, correlation entropy, and local correlation entropy for free semigroup actions under different conditions.

We study a planar random motion (big (X(t),,Y(t)big )) with orthogonal directions, where the direction switches are governed by a homogeneous Poisson process. At each Poisson event, the moving particle turns clockwise or counterclockwise according to a rule which depends on the current direction. We prove that the components of the vector (big (X(t),,Y(t)big )) can be represented as linear combinations of two independent telegraph processes with different intensities. The exact distribution of (big (X(t),,Y(t)big )) is then obtained both in the interior of the support and on its boundary, where a singular component is present. We show that, in the hydrodynamic limit, the process behaves as a planar Brownian motion with correlated components. The distribution of the time spent by the process moving vertically is then studied. We obtain its exact distribution and discuss its hydrodynamic limit. In particular, in the limiting case, the process (big (X(t),,Y(t)big )) spends half of the time moving vertically.