128 research outputs found
Condensate formation in a zero-range process with random site capacities
We study the effect of quenched disorder on the zero-range process (ZRP), a
system of interacting particles undergoing biased hopping on a one-dimensional
periodic lattice, with the disorder entering through random capacities of
sites. In the usual ZRP, sites can accommodate an arbitrary number of
particles, and for a class of hopping rates and high enough density, the steady
state exhibits a condensate which holds a finite fraction of the total number
of particles. The sites of the disordered zero-range process considered here
have finite capacities chosen randomly from the Pareto distribution. From the
exact steady state measure of the model, we identify the conditions for
condensate formation, in terms of parameters that involve both interactions
(through the hop rates) and randomness (through the distribution of the site
capacities). Our predictions are supported by results obtained from a direct
numerical sampling of the steady state and from Monte Carlo simulations. Our
study reveals that for a given realization of disorder, the condensate can
relocate on the subset of sites with largest capacities. We also study
sample-to-sample variation of the critical density required to observe
condensation, and show that the corresponding distribution obeys scaling, and
has a Gaussian or a Levy-stable form depending on the values of the relevant
parameters.Comment: Contribution to the JStatMech Special Issue dedicated to the Galileo
Galilei Institute, Florence Workshop "Advances in nonequilibrium statistical
mechanics",v2: close to the published versio
Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation
We develop a new fast-diffusion approximation for the kinetics of deposition
of extended objects on a linear substrate, accompanied by diffusional
relaxation. This new approximation plays the role of the mean-field theory for
such processes and is valid over a significantly larger range than an earlier
variant, which was based on a mapping to chemical reactions. In particular,
continuum-limit off-lattice deposition is described naturally within our
approximation. The criteria for the applicability of the mean-field theory are
derived. While deposition of dimers, and marginally, trimers, is affected by
fluctuations, we find that the k-mer deposition kinetics is asymptotically
mean-field like for all k=4,5,..., where the limit k->infinity, when properly
defined, describes deposition-diffusion kinetics in the continuum.Comment: 18 page
Shock probes in a one-dimensional Katz-Lebowitz-Spohn model
We consider shock probes in a one-dimensional driven diffusive medium with
nearest neighbor Ising interaction (KLS model). Earlier studies based on an
approximate mapping of the present system to an effective zero-range process
concluded that the exponents characterising the decays of several static and
dynamical correlation functions of the probes depend continuously on the
strength of the Ising interaction. On the contrary, our numerical simulations
indicate that over a substantial range of the interaction strength, these
exponents remain constant and their values are the same as in the case of no
interaction (when the medium executes an ASEP). We demonstrate this by
numerical studies of several dynamical correlation functions for two probes and
also for a macroscopic number of probes. Our results are consistent with the
expectation that the short-ranged correlations induced by the Ising interaction
should not affect the large time and large distance properties of the system,
implying that scaling forms remain the same as in the medium with no
interactions present.Comment: Accepted in Physical Review
Small metal particles and the ideal Fermi gas
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