115 research outputs found
Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems
We calculate the spectrum of Lyapunov exponents for a point particle moving
in a random array of fixed hard disk or hard sphere scatterers, i.e. the
disordered Lorentz gas, in a generic nonequilibrium situation. In a large
system which is finite in at least some directions, and with absorbing boundary
conditions, the moving particle escapes the system with probability one.
However, there is a set of zero Lebesgue measure of initial phase points for
the moving particle, such that escape never occurs. Typically, this set of
points forms a fractal repeller, and the Lyapunov spectrum is calculated here
for trajectories on this repeller. For this calculation, we need the solution
of the recently introduced extended Boltzmann equation for the nonequilibrium
distribution of the radius of curvature matrix and the solution of the standard
Boltzmann equation. The escape-rate formalism then gives an explicit result for
the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev
Entropy Production in a Persistent Random Walk
We consider a one-dimensional persisent random walk viewed as a deterministic
process with a form of time reversal symmetry. Particle reservoirs placed at
both ends of the system induce a density current which drives the system out of
equilibrium. The phase space distribution is singular in the stationary state
and has a cumulative form expressed in terms of generalized Takagi functions.
The entropy production rate is computed using the coarse-graining formalism of
Gaspard, Gilbert and Dorfman. In the continuum limit, we show that the value of
the entropy production rate is independent of the coarse-graining and agrees
with the phenomenological entropy production rate of irreversible
thermodynamics.Comment: 21 pages, 8 figures, to appear in Physica
Thermodynamic relations in a driven lattice gas: numerical exprements
We explore thermodynamic relations in non-equilibrium steady states with
numerical experiments on a driven lattice gas. After operationally defining the
pressure and chemical potential in the driven lattice gas, we confirm
numerically the validity of the integrability condition (the Maxwell relation)
for the two quantities whose values differ from those for an equilibrium
system. This implies that a free energy function can be constructed for the
non-equilibrium steady state that we consider. We also investigate a
fluctuation relation associated with this free energy function. Our result
suggests that the compressibility can be expressed in terms of density
fluctuations even in non-equilibrium steady states.Comment: 4 pages, 4 figure
Viscosity in the escape-rate formalism
We apply the escape-rate formalism to compute the shear viscosity in terms of
the chaotic properties of the underlying microscopic dynamics. A first passage
problem is set up for the escape of the Helfand moment associated with
viscosity out of an interval delimited by absorbing boundaries. At the
microscopic level of description, the absorbing boundaries generate a fractal
repeller. The fractal dimensions of this repeller are directly related to the
shear viscosity and the Lyapunov exponent, which allows us to compute its
values. We apply this method to the Bunimovich-Spohn minimal model of viscosity
which is composed of two hard disks in elastic collision on a torus. These
values are in excellent agreement with the values obtained by other methods
such as the Green-Kubo and Einstein-Helfand formulas.Comment: 16 pages, 16 figures (accepted in Phys. Rev. E; October 2003
Long-Ranged Correlations in Sheared Fluids
The presence of long-ranged correlations in a fluid undergoing uniform shear
flow is investigated. An exact relation between the density autocorrelation
function and the density-mometum correlation function implies that the former
must decay more rapidly than , in contrast to predictions of simple mode
coupling theory. Analytic and numerical evaluation of a non-perturbative
mode-coupling model confirms a crossover from behavior at ''small''
to a stronger asymptotic power-law decay. The characteristic length scale is
where is the sound damping
constant and is the shear rate.Comment: 15 pages, 2 figures. Submitted to PR
Characteristics of Quantum-Classical Correspondence for Two Interacting Spins
The conditions of quantum-classical correspondence for a system of two
interacting spins are investigated. Differences between quantum expectation
values and classical Liouville averages are examined for both regular and
chaotic dynamics well beyond the short-time regime of narrow states. We find
that quantum-classical differences initially grow exponentially with a
characteristic exponent consistently larger than the largest Lyapunov exponent.
We provide numerical evidence that the time of the break between the quantum
and classical predictions scales as log(), where is
a characteristic system action. However, this log break-time rule applies only
while the quantum-classical deviations are smaller than order hbar. We find
that the quantum observables remain well approximated by classical Liouville
averages over long times even for the chaotic motions of a few
degree-of-freedom system. To obtain this correspondence it is not necessary to
introduce the decoherence effects of a many degree-of-freedom environment.Comment: New introduction, accepted in Phys Rev A (May 2001 issue), 12 latex
figures, 3 ps figure
A diffusive system driven by a battery or by a smoothly varying field
We consider the steady state of a one dimensional diffusive system, such as
the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at
the origin or by a smoothly varying field along the ring. The battery appears
as the limiting case of a smoothly varying field, when the field becomes a
delta function at the origin. We find that in the scaling limit, the long range
pair correlation functions of the system driven by a battery turn out to be
very different from the ones known in the steady state of the SSEP maintained
out of equilibrium by contact with two reservoirs, even when the steady state
density profiles are identical in both models
Anomalous Pressure in Fluctuating Shear Flow
We investigate how the pressure in fluctuating shear flow depends on the
shear rate and on the system size by studying fluctuating hydrodynamics
under shear conditions. We derive anomalous forms of the pressure for two
limiting values of the dimensionless parameter , where
is the kinematic viscosity. In the case , the pressure is not an
intensive quantity because of the influence of the long-range spatial
correlations of momentum fluctuations. In the other limit , the
long-range correlations are suppressed at large distances, and the pressure is
intensive. In this case, however, there is the interesting effect that the
non-equilibrium correction to the pressure is proportional to , which
was previously obtained with the projection operator method [K. Kawasaki and J.
D. Gunton, Phys. Rev. {\bf A 8}, 2048, (1973)].Comment: Breakdown of the intensivity of pressure is emphasized. Fig.1 and
references added; accepted for publication as a Rapid Communication in Phys.
Rev.
Theory of Disordered Itinerant Ferromagnets I: Metallic Phase
A comprehensive theory for electronic transport in itinerant ferromagnets is
developed. We first show that the Q-field theory used previously to describe a
disordered Fermi liquid also has a saddle-point solution that describes a
ferromagnet in a disordered Stoner approximation. We calculate transport
coefficients and thermodynamic susceptibilities by expanding about the saddle
point to Gaussian order. At this level, the theory generalizes previous
RPA-type theories by including quenched disorder. We then study soft-mode
effects in the ferromagnetic state in a one-loop approximation. In
three-dimensions, we find that the spin waves induce a square-root frequency
dependence of the conductivity, but not of the density of states, that is
qualitatively the same as the usual weak-localization effect induced by the
diffusive soft modes. In contrast to the weak-localization anomaly, this effect
persists also at nonzero temperatures. In two-dimensions, however, the spin
waves do not lead to a logarithmic frequency dependence. This explains
experimental observations in thin ferromagnetic films, and it provides a basis
for the construction of a simple effective field theory for the transition from
a ferromagnetic metal to a ferromagnetic insulator.Comment: 15pp., REVTeX, 2 eps figs, final version as publishe
Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
In this paper we present a self-contained macroscopic description of
diffusive systems interacting with boundary reservoirs and under the action of
external fields. The approach is based on simple postulates which are suggested
by a wide class of microscopic stochastic models where they are satisfied. The
description however does not refer in any way to an underlying microscopic
dynamics: the only input required are transport coefficients as functions of
thermodynamic variables, which are experimentally accessible. The basic
postulates are local equilibrium which allows a hydrodynamic description of the
evolution, the Einstein relation among the transport coefficients, and a
variational principle defining the out of equilibrium free energy. Associated
to the variational principle there is a Hamilton-Jacobi equation satisfied by
the free energy, very useful for concrete calculations. Correlations over a
macroscopic scale are, in our scheme, a generic property of nonequilibrium
states. Correlation functions of any order can be calculated from the free
energy functional which is generically a non local functional of thermodynamic
variables. Special attention is given to the notion of equilibrium state from
the standpoint of nonequilibrium.Comment: 21 page
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