Journal of Statistical Physics最新文献

We show that a modification of the proof of our paper Coquille et al. (J. Stat. Phys. 172(5), 1210–1222 (2018)), in the spirit of Fröhlich and Pfister (Commun. Math. Phys. 81, 277–298 (1981)), shows delocalisation in the long-range Discrete Gaussian Chain, and generalisations thereof, for any decay power (alpha >2) and at all temperatures. The argument proceeds by contradiction: any shift-invariant and localised measure (in the (L^1) sense), is a convex combination of ergodic localised measures. But the latter cannot exist: on one hand, by the ergodic theorem, the average of the field over growing boxes would be almost surely bounded ; on the other hand the measure would be absolutely continuous with respect to its height-shifted translates, as a simple relative entropy computation shows. This leads to a contradiction and answers, in a non-quantitative way, an open question stated in a recent paper of C. Garban (Invisibility of the integers for the discrete Gaussian Chain via a caffarelli-silvestre extension of the discrete fractional laplacian. Preprint arXiv:2312.04536v2, (2023)).

Inspired by different stochastic mechanisms, such as the two-sided motion of ribosomes seen during the initiation of mRNA translation, which is backed by their decay, we investigate a totally asymmetric simple exclusion process with open boundaries in a bidirectional setting where two oppositely charged species of particles move opposite to each other and locally reset to the respective entry site. The steady-state characteristics, such as density profiles and phase diagrams, are investigated theoretically under the mean-field framework. The introduction of resetting into the system produces non-trivial effects in the form of two novel asymmetric phases that appear in the phase diagram. The system possesses several different combinations of symmetric phases as well as asymmetric phases for different resetting rates. A rich behavior is observed in the system, emphasizing the occurrence of spontaneous symmetry-breaking phenomena even in the small resetting regime. Moreover, the significance of the resetting rate is analyzed on the domain wall, and it is found that one of the stationary phases with a localized domain wall vanishes for a substantial resetting rate. Due to the interaction of both species at the boundaries, the consequences of the resetting dynamics on the boundary densities are also investigated. All the findings, including finite-system size, are thoroughly validated by the Monte Carlo simulations.

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a source term. Different from the usual boundary conditions introduced in Bardos et al (Commun Partial Differ Equ 4(9):1017–1034, https://doi.org/10.1080/03605307908820117, 1979) and Otto (C R Acad Sci Paris 322(1):729–734, 1996), discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme.

In this paper, we investigate the impact of bond-dilution disorder on the critical behavior of the stochastic SIR model. Monte Carlo simulations were conducted using square lattices with first- and second-nearest neighbor interactions. Quenched bond-diluted lattice disorder was introduced into the systems, allowing them to evolve over time. By employing percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the model for different bond-dilution rates (p). An examination of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was performed to ascertain the universality class of the model. The simulation results strongly indicate that the present model belongs to a new universality class distinct from that of 2D dynamical percolation, depending on the specific p value under consideration.

Approach of mesoscopic state variables to time independent equilibrium sates (zero law of thermodynamics) gives birth to the classical equilibrium thermodynamics. Approach of fluxes and forces to fixed points (equilibrium fluxes and forces) that drive reduced mesoscopic dynamics gives birth to the rate thermodynamics that is applicable to driven systems. We formulate the rate thermodynamics and dynamics, investigate its relation to the classical thermodynamics, to extensions involving more details, to the hierarchy reformulations of dynamical theories, and to the Onsager variational principle. We also compare thermodynamic and dynamic critical behavior observed in closed and open systems. Dynamics and thermodynamics of the van der Waals gas provides an illustration.

We consider the symmetric Markov random flight, also called the persistent random walk, performed by a particle that moves at constant finite speed in the Euclidean space (mathbb {R}^m, ; mge 2,) and changes its direction at Poisson-distributed time instants by taking it at random according to the uniform distribution on the surface of the unit ((m-1))-dimensional sphere. Such stochastic motion has become a very popular object of modern statistical physics because it can serve as an appropriate model for describing the isotropic finite-velocity transport in multidimensional Euclidean spaces. In recent decade this approach was also developed in the framework of the run-and-tumble theory. In this article we study one of the most important characteristics of the multidimensional symmetric Markov random flight, namely, its characteristic function. We derive two series representations of the characteristic function of the process with respect to Bessel functions with variable indices and with respect to the powers of time variable. The coefficients of these series are given by recurrent relations, as well as in the form of special determinants. As an application of these results, an asymptotic formula for the second moment function (mu _{(2,2,2)}(t), ; t>0,) of the three-dimensional Markov random flight, is presented. The moment function (mu _{(2,0,0)}(t), ; t>0,) is obtained in an explicit form.

The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with the in-flow, diffuse-reflection, or specular-reflection boundary condition. Using a novel kernel estimate, we demonstrate the optimal (L^2) diffusive limit in the presence of both initial and boundary layers. Previously, this result was only proved for convex domains when the time variable is involved. Our approach is highly robust, making it applicable to all basic types of physical boundary conditions.

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability (1-f(t)). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation (-gamma ), where (gamma in [0,1)). We also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

For (alpha ge 1), let (g:{mathbb {N}}rightarrow {mathbb {R}}_+) be given by (g(0)=0), (g(1)=1), (g(k)=(k/k-1)^alpha ), (kge 2). Consider the homogeneous zero range process on a discrete set in which a particle jumps from a site x, occupied by k particles, to site y with rate (g(k)p(y-x)) for some fixed probability (p:{mathbb {Z}}rightarrow [0,1]). Armendáriz and Loulakis (Probab Theory Relat Fields 145:175–188, 2009, https://doi.org/10.1007/s00440-008-0165-7) proved a strong form of the equivalence of ensembles for the invariant measure of the supercritical zero range process with (alpha >2). We generalize their result to all (alpha ge 1).

We rigorously prove that the local conserved quantities in the one-dimensional Hubbard model are uniquely determined for each locality up to the freedom to add lower-order ones. From this, we can conclude that the local conserved quantities are exhausted by those obtained from the expansion of the transfer matrix.