On time's arrow in Ehrenfest models with reversible deterministic dynamics

We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equilibrium states and vice versa is calculated. We find that average times for transition to non-equilibrium always scale exponentially with the system size, whereas the time scale for relaxation to equilibrium depends on microscopic dynamics. To illustrate this, we also look at deterministic and stochastic versions of the Ehrenfest model with a distribution of microscopic relaxation times.Comment: 6 pages, 7 figures, revte

Heat conduction in disordered harmonic lattices with energy conserving noise

We study heat conduction in a harmonic crystal whose bulk dynamics is supplemented by random reversals (flips) of the velocity of each particle at a rate $\lambda$. The system is maintained in a nonequilibrium stationary state(NESS) by contacts with Langevin reservoirs at different temperatures. We show that the one-body and pair correlations in this system are the same (after an appropriate mapping of parameters) as those obtained for a model with self-consistent reservoirs. This is true both for the case of equal and random(quenched) masses. While the heat conductivity in the NESS of the ordered system is known explicitly, much less is known about the random mass case. Here we investigate the random system, with velocity flips. We improve the bounds on the Green-Kubo conductivity obtained by C.Bernardin. The conductivity of the 1D system is then studied both numerically and analytically. This sheds some light on the effect of noise on the transport properties of systems with localized states caused by quenched disorder.Comment: 19 pages, 8 figure

Percolation in the Harmonic Crystal and Voter Model in three dimensions

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential, $U=\frac{J}{2} \sum_{} (\phi(x) - \phi(y))^2$, $x,y \in \mathbb{Z}^3$, $J > 0$ and $\phi(x) \in \mathbb{R}$, a scalar height variable, and define occupation variables $\rho_h(x) =1,(0)$ for $\phi(x) > h (<h)$. The probability $p$ of a site being occupied, is then a function of $h$. In the voter model we consider the stationary measure, in which each site is either occupied or empty, with probability $p$. In both cases the truncated pair correlation of the occupation variables, $G(x-y)$, decays asymptotically like $|x-y|^{-1}$. Using some novel Monte Carlo simulation methods and finite size scaling we find accurate values of $p_c$ as well as the critical exponents for these systems. The latter are different from that of independent percolation in $d=3$, as expected from the work of Weinrib and Halperin [WH] for the percolation transition of systems with $G(r) \sim r^{-a}$ [A. Weinrib and B. Halperin, Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent $\nu$ is very close to the predicted value of 2 supporting the conjecture by WH that $\nu= \frac{2}{a}$ is exact.Comment: 8 figures. new version significantly different from the old one, includes new results, figures et

Multicomponent fluids of hard hyperspheres in odd dimensions

Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlations functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein--Zernike equation coupled with the Percus--Yevick closure, thus extending to arbitrary odd dimension the solution for hard-sphere mixtures [J. L. Lebowitz, Phys.\ Rev.\ \textbf{133}, 895 (1964)]. Explicit evaluations for binary mixtures in five dimensions are performed. The results are compared with computer simulations and a good agreement is found.Comment: 16 pages, 8 figures; v2: slight change of notatio

From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example

Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of mutually interacting subsystem and heat bath, and assume that the whole system is initially in a pure state (which can be far from equilibrium) with small energy fluctuation. Under the "hypothesis of equal weights for eigenstates", we derive the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses.Comment: LaTeX, 8 pages, no figures. The title, abstract and some discussions are modified to stress physical motivation of the work. References are added to [2]. This version will appear in Phys. Rev. Lett. There is an accompanying unpublished note (cond-mat/9707255

Product Measure Steady States of Generalized Zero Range Processes

We establish necessary and sufficient conditions for the existence of factorizable steady states of the Generalized Zero Range Process. This process allows transitions from a site $i$ to a site $i+q$ involving multiple particles with rates depending on the content of the site $i$, the direction $q$ of movement, and the number of particles moving. We also show the sufficiency of a similar condition for the continuous time Mass Transport Process, where the mass at each site and the amount transferred in each transition are continuous variables; we conjecture that this is also a necessary condition.Comment: 9 pages, LaTeX with IOP style files. v2 has minor corrections; v3 has been rewritten for greater clarit