2,114 research outputs found
Field Driven Thermostated System : A Non-Linear Multi-Baker Map
In this paper, we discuss a simple model for a field driven, thermostated
random walk that is constructed by a suitable generalization of a multi-baker
map. The map is a usual multi-baker, but perturbed by a thermostated external
field that has many of the properties of the fields used in systems with
Gaussian thermostats. For small values of the driving field, the map is
hyperbolic and has a unique SRB measure that we solve analytically to first
order in the field parameter. We then compute the positive and negative
Lyapunov exponents to second order and discuss their relation to the transport
properties. For higher values of the parameter, this system becomes
non-hyperbolic and posseses an attractive fixed point.Comment: 6 pages + 5 figures, to appear in Phys. Rev.
Chaotic properties of systems with Markov dynamics
We present a general approach for computing the dynamic partition function of
a continuous-time Markov process. The Ruelle topological pressure is identified
with the large deviation function of a physical observable. We construct for
the first time a corresponding finite Kolmogorov-Sinai entropy for these
processes. Then, as an example, the latter is computed for a symmetric
exclusion process. We further present the first exact calculation of the
topological pressure for an N-body stochastic interacting system, namely an
infinite-range Ising model endowed with spin-flip dynamics. Expressions for the
Kolmogorov-Sinai and the topological entropies follow.Comment: 4 pages, to appear in the Physical Review Letter
Distribution of label spacings for genome mapping in nanochannels
In genome mapping experiments, long DNA molecules are stretched by confining
them to very narrow channels, so that the locations of sequence-specific
fluorescent labels along the channel axis provide large-scale genomic
information. It is difficult, however, to make the channels narrow enough so
that the DNA molecule is fully stretched. In practice its conformations may
form hairpins that change the spacings between internal segments of the DNA
molecule, and thus the label locations along the channel axis. Here we describe
a theory for the distribution of label spacings that explains the heavy tails
observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl
Field dependent collision frequency of the two-dimensional driven random Lorentz gas
In the field-driven, thermostatted Lorentz gas the collision frequency
increases with the magnitude of the applied field due to long-time
correlations. We study this effect with computer simulations and confirm the
presence of non-analytic terms in the field dependence of the collision
frequency as predicted by kinetic theory.Comment: 6 pages, 2 figures. Submitted to Phys. Rev.
Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime
We consider the time evolution of a wave packet representing a quantum
particle moving in a geometrically open billiard that consists of a number of
fixed hard-disk or hard-sphere scatterers. Using the technique of multiple
collision expansions we provide a first-principle analytical calculation of the
time-dependent autocorrelation function for the wave packet in the high-energy
diffraction regime, in which the particle's de Broglie wave length, while being
small compared to the size of the scatterers, is large enough to prevent the
formation of geometric shadow over distances of the order of the particle's
free flight path. The hard-disk or hard-sphere scattering system must be
sufficiently dilute in order for this high-energy diffraction regime to be
achievable. Apart from the overall exponential decay, the autocorrelation
function exhibits a generally complicated sequence of relatively strong peaks
corresponding to partial revivals of the wave packet. Both the exponential
decay (or escape) rate and the revival peak structure are predominantly
determined by the underlying classical dynamics. A relation between the escape
rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the
counterpart classical system, previously known for hard-disk billiards, is
strengthened by generalization to three spatial dimensions. The results of the
quantum mechanical calculation of the time-dependent autocorrelation function
agree with predictions of the semiclassical periodic orbit theory.Comment: 24 pages, 13 figure
Non-equilibrium Lorentz gas on a curved space
The periodic Lorentz gas with external field and iso-kinetic thermostat is
equivalent, by conformal transformation, to a billiard with expanding
phase-space and slightly distorted scatterers, for which the trajectories are
straight lines. A further time rescaling allows to keep the speed constant in
that new geometry. In the hyperbolic regime, the stationary state of this
billiard is characterized by a phase-space contraction rate, equal to that of
the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where
phase-space contraction occurs in the bulk, the phase-space contraction rate
here takes place at the periodic boundaries
Lattice gas with ``interaction potential''
We present an extension of a simple automaton model to incorporate non-local
interactions extending over a spatial range in lattice gases. {}From the
viewpoint of Statistical Mechanics, the lattice gas with interaction range may
serve as a prototype for non-ideal gas behavior. {}From the density
fluctuations correlation function, we obtain a quantity which is identified as
a potential of mean force. Equilibrium and transport properties are computed
theoretically and by numerical simulations to establish the validity of the
model at macroscopic scale.Comment: 12 pages LaTeX, figures available on demand ([email protected]
The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy
per particle for a dilute gas in equilibrium. For an equilibrium system, the KS
entropy, h_KS is the sum of all of the positive Lyapunov exponents
characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is
the number of particles in the gas. This quantity has a density expansion of
the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the
single-particle collision frequency and \tilde{n} is the reduced number density
of the gas. The theoretical values for the coefficients a and b are compared
with the results of computer simulations, with excellent agreement for a, and
less than satisfactory agreement for b. Possible reasons for this difference in
b are discussed.Comment: 15 pages, 2 figures, submitted to Phys. Rev.
Chaos properties and localization in Lorentz lattice gases
The thermodynamic formalism of Ruelle, Sinai, and Bowen, in which chaotic
properties of dynamical systems are expressed in terms of a free energy-type
function - called the topological pressure - is applied to a Lorentz Lattice
Gas, as typical for diffusive systems with static disorder. In the limit of
large system sizes, the mechanism and effects of localization on large clusters
of scatterers in the calculation of the topological pressure are elucidated and
supported by strong numerical evidence. Moreover it clarifies and illustrates a
previous theoretical analysis [Appert et al. J. Stat. Phys. 87,
chao-dyn/9607019] of this localization phenomenon.Comment: 32 pages, 19 Postscript figures, submitted to PR
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