Journal of Statistical Physics最新文献

A new phase space path integral representation of quantum density of states (DOS) was derived for a strongly coupled plasma media representing hydrogen plasma and two-component Coulomb system with uniformly distributed in space uncorrelated positive charges (“protons”) simulating a neutralizing background (“OCP”). A path integral Monte Carlo approach was used for the calculation of DOS, energy and momentum distribution functions as well as spin–resolved radial distribution functions (RDFs). The RDFs for electrons with the same spin projection revealed exchange–correlation cavities. For a two-component hydrogen plasma (TCP) the Coulomb attraction results in the appearance of high peaks on the proton–electron RDFs at small interparticle distances, while for the “OCP” the analogous RDFs demonstrate an unexpected significant drop arising due to a three–particle effect caused by the electron repulsion preventing for any two electrons to be in the vicinity of any uncorrelated charge. At negative plasma energy the “OCP” DOS is a fast-decaying function, while in hydrogen plasma at a temperature of the order of 1 (textrm{Ry} = 0.5text {Ha}approx 13.6) eV the DOS shows a well-pronounced peak related to the bound states. Quantum effects make momentum distribution functions non-maxwellian with a power-law high-momentum asymptotics (“quantum tails”) even under the condition of thermodynamic equilibrium.

We study the Poisson Boolean percolation model on Ahlfors regular metric measure spaces, extending fundamental results from the Euclidean spaces to more general geometric settings. Ahlfors regular space is a metric measure space that has a polynomial growth rate of metric balls. Our main result establishes that for s-Ahlfors regular spaces, the model exhibits a subcritical regime (no infinite clusters for small intensities) if and only if the radius distribution has a finite s-th moment, generalizing Gouéré’s result for the Euclidean spaces. We prove both directions: when an s-th moment is finite, we show that subcritical behavior exists using geometric properties of Ahlfors regular spaces, particularly the doubling property and the uniform perfectness. Conversely, when an s-th moment diverges, we demonstrate that infinite clusters occur almost surely for any positive intensity. The key technical innovation lies in handling the geometric challenges absent in Euclidean spaces, such as potentially empty annuli between concentric balls. We overcome this using uniform perfectness, which guarantees nonempty annuli under sufficient expansion, combined with doubling properties to control covering numbers. Our results apply broadly to Riemannian manifolds with nonnegative Ricci curvature, ultrametric spaces, unbounded Sierpinski gaskets, and snowflake constructions of Ahlfors regular spaces.

Run-and-Tumble Particles (RTPs) are a key model of active matter. They are characterized by alternating phases of linear travel and random direction reshuffling. By this dynamic behavior, they break time reversibility and energy conservation at the microscopic level. It leads to complex out-of-equilibrium phenomena such as collective motion, pattern formation, and motility-induced phase separation (MIPS). In this work, we study two fundamental dynamical models of a pair of RTPs with jamming interactions and provide a rigorous link between their discrete- and continuous-space descriptions. We demonstrate that as the lattice spacing vanishes, the discrete models converge to a continuous RTP model on the torus, described by a Piecewise Deterministic Markov Process (PDMP). This establishes that the invariant measures of the discrete models converge to that of the continuous model, which reveals finite mass at jamming configurations and exponential decay away from them. This indicates effective attraction, which is consistent with MIPS. Furthermore, we quantitatively explore the convergence towards the invariant measure. Such convergence study is critical for understanding and characterizing how MIPS emerges over time. Because RTP systems are non-reversible, usual methods may fail or are limited to qualitative results. Instead, we adopt a coupling approach to obtain more accurate, non-asymptotic bounds on mixing times. The findings thus provide deeper theoretical insights into the mixing times of these RTP systems, revealing the presence of both persistent and diffusive regimes.

In this article, we study the entropy dynamics of the Heisenberg spin chain with binary bond disorder. We first develop a new method that integrates the purification scheme and the time-evolving block decimation (TEBD) algorithm, named ancillary TEBD, to study the entropy dynamics of spin chains with binary bond disorder. Secondly, with the support of exact diagonalization (ED), we calculate the multifractal dimension of the eigenstates of the bond-disordered Heisenberg chain and the quench dynamics of the inverse participation ratio (IPR), finding that the dependence of the multifractal dimension on the strength of the disorder shows no critical behavior, ruling out the existence of the many-body localization transition in the system. Then, using the ED and the ancillary TEBD method, we study the entropy dynamics of the Heisenberg chain with binary bond disorder and ascertain that the quench dynamics of the entanglement entropy can be divided into four different stages, which are attributed to the competition of the spin interaction and the disorder. Our results propose a new mechanism for the generation of logarithmic scaling behavior of entropy dynamics in disordered systems. Finally, using the ancillary TEBD method, we numerically prove the existence of the transient Mpemba effect in the bond-disordered Heisenberg chain.

The continuous injection of energy in a stationary gas creates a shock wave that propagates radially outwards. We study the hydrodynamics of this disturbance using event driven molecular dynamics of a hard-sphere gas in two and three dimensions, the numerical solution of the Euler equation with a virial equation of state for the gas, and the numerical solution of the Navier-Stokes equations, for the cases when the driving is localized in space and when it is uniform throughout the shock. We show that the results from the Euler equation do not agree with the data from hard-sphere simulations when the driving is uniform and has singularities when the driving is localized. Including dissipative terms through the Navier-Stokes equations results in reasonably good description of the data, when the coefficients of dissipation are chosen parametrically.

The Brownian motion in water–ethanol mixtures exhibits abnormally large displacements. Using falling-ball viscometry applied to colloidal particles, we experimentally verified that no anomaly exists in the viscosity coefficient of the solution. We concluded that the anomalous Brownian motion displacement is due to anomalous thermal fluctuations, not viscous forces. We proposed that the coupling of rotational and translational Brownian motion may result in anomalous thermal fluctuations. The viscosity fluctuation converts rotational motion into translational motion, and the displacement increases by that amount. The anomalous thermal disturbance continues for the relaxation time of rotational Brownian motion, which produces a type of memory effect.

We investigate the splash phenomenon resulting from the energy input at the interface between a vacuum and an inhomogeneous gas with density profile (rho (r) = rho _0 r^{-beta }). The energy input causes the formation of ballistic spatters that propagate into the vacuum, leading to a decay of the total energy in the inhomogeneous medium following a power law, (E(t) sim t^{-delta _s}). We determine exactly the exponents (delta _s) by solving the Euler equation using a self-similar solution of the second kind for different values of (beta ). These exponents are further validated through event-driven molecular dynamics simulations. The determination of these exponents also allows us to numerically determine the spatio-temporal dependence of the density, velocity and temperature.

In this work, we consider the incompressible generalized Navier-Stokes-Voigt equations in a bounded domain (mathcal {O}subset mathbb {R}^d), (dge 2), driven by a multiplicative Gaussian noise. The considered momentum equation is given by:

In the case of (d=2,3), (varvec{u}) accounts for the velocity field, (pi ) is the pressure, (varvec{f}) is a body force and the final term represents the stochastic forces. Here, (kappa ) and (nu ) are given positive constants that account for the kinematic viscosity and relaxation time, and the power-law index p is another constant (assumed (p>1)) that characterizes the flow. We use the usual notation (textbf{I}) for the unit tensor and (textbf{D}(varvec{u}):=frac{1}{2}left( nabla varvec{u} + (nabla varvec{u})^{top }right) ) for the symmetric part of velocity gradient. For (pin big (frac{2d}{d+2},infty big )), we first prove the existence of a martingale solution. Then we show the pathwise uniqueness of solutions. We employ the classical Yamada-Watanabe theorem to ensure the existence of a unique probabilistic strong solution.

We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which that limit shape can be shown to be differentiable. We then describe examples of continuous first passage percolation models that fit into this framework. The first example is of a family of Riemannian first passage percolation models and the second is a discrete time model based on Poissonian points.

Backwards geodesics for TASEP were introduced in [30]. We consider flat initial conditions and show that under proper scaling the end-point of the geodesic converges to maximizer argument of the (hbox {Airy}_2) process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.