1,370 research outputs found
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 . 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,
, , and , a scalar height variable, and define
occupation variables for . The probability
of a site being occupied, is then a function of . In the voter model we
consider the stationary measure, in which each site is either occupied or
empty, with probability . In both cases the truncated pair correlation of
the occupation variables, , decays asymptotically like .
Using some novel Monte Carlo simulation methods and finite size scaling we find
accurate values of as well as the critical exponents for these systems.
The latter are different from that of independent percolation in , as
expected from the work of Weinrib and Halperin [WH] for the percolation
transition of systems with [A. Weinrib and B. Halperin,
Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent
is very close to the predicted value of 2 supporting the conjecture by WH
that 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 to a site involving multiple particles
with rates depending on the content of the site , the direction 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
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