6,631 research outputs found
Absence of phase coexistence in disordered exclusion processes with bypassing
Adding quenched disorder to the one-dimensional asymmetric exclusion process
is known to always induce phase separation. To test the robustness of this
result, we introduce two modifications of the process that allow particles to
bypass defect sites. In the first case, particles are allowed to jump l sites
ahead with the probability p_l ~ l^-(1+sigma), where sigma>1. By using Monte
Carlo simulations and the mean-field approach, we show that phase coexistence
may be absent up to enormously large system sizes, e.g. lnL~50, but is present
in the thermodynamic limit, as in the short-range case. In the second case, we
consider the exclusion process on a quadratic lattice with symmetric and
totally asymmetric hopping perpendicular to and along the direction of driving,
respectively. We show that in an anisotropic limit of this model a regime may
be found where phase coexistence is absent.Comment: 18 pages, 10 figures, to appear in JSTA
Generic principles of active transport
Nonequilibrium collective motion is ubiquitous in nature and often results in
a rich collection of intringuing phenomena, such as the formation of shocks or
patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase
transitions. These stochastic many-body features characterize transport
processes in biology, soft condensed matter and, possibly, also in nanoscience.
Inspired by these applications, a wide class of lattice-gas models has recently
been considered. Building on the celebrated {\it totally asymmetric simple
exclusion process} (TASEP) and a generalization accounting for the exchanges
with a reservoir, we discuss the qualitative and quantitative nonequilibrium
properties of these model systems. We specifically analyze the case of a
dimeric lattice gas, the transport in the presence of pointwise disorder and
along coupled tracks.Comment: 21 pages, 10 figures. Pedagogical paper based on a lecture delivered
at the conference on "Stochastic models in biological sciences" (May 29 -
June 2, 2006 in Warsaw). For the Banach Center Publication
Phase Transitions in one-dimensional nonequilibrium systems
The phenomenon of phase transitions in one-dimensional systems is discussed.
Equilibrium systems are reviewed and some properties of an energy function
which may allow phase transitions and phase ordering in one dimension are
identified. We then give an overview of the one-dimensional phase transitions
which we have been studied in nonequilibrium systems. A particularly simple
model, the zero-range process, for which the steady state is know exactly as a
product measure, is discussed in some detail. Generalisations of the model, for
which a product measure still holds, are also discussed. We analyse in detail a
condensation phase transition in the model and show how conditions under which
it may occur may be related to the existence of an effective long-range energy
function. Although the zero-range process is not well known within the physics
community, several nonequilibrium models have been proposed that are examples
of a zero-range process, or closely related to it, and we review these
applications here.Comment: latex, 28 pages, review article; references update
The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm
in non-equilibrium statistical mechanics. We review exact results for the ASEP
obtained by Bethe ansatz and put emphasis on the algebraic properties of this
model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP
are derived from the algebraic Bethe ansatz. Using these equations we explain
how to calculate the spectral gap of the model and how global spectral
properties such as the existence of multiplets can be predicted. An extension
of the Bethe ansatz leads to an analytic expression for the large deviation
function of the current in the ASEP that satisfies the Gallavotti-Cohen
relation. Finally, we describe some variants of the ASEP that are also solvable
by Bethe ansatz.
Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent
advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and
J. Feinberg editor
Parallel Coupling of Symmetric and Asymmetric Exclusion Processes
A system consisting of two parallel coupled channels where particles in one
of them follow the rules of totally asymmetric exclusion processes (TASEP) and
in another one move as in symmetric simple exclusion processes (SSEP) is
investigated theoretically. Particles interact with each other via hard-core
exclusion potential, and in the asymmetric channel they can only hop in one
direction, while on the symmetric lattice particles jump in both directions
with equal probabilities. Inter-channel transitions are also allowed at every
site of both lattices. Stationary state properties of the system are solved
exactly in the limit of strong couplings between the channels. It is shown that
strong symmetric couplings between totally asymmetric and symmetric channels
lead to an effective partially asymmetric simple exclusion process (PASEP) and
properties of both channels become almost identical. However, strong asymmetric
couplings between symmetric and asymmetric channels yield an effective TASEP
with nonzero particle flux in the asymmetric channel and zero flux on the
symmetric lattice. For intermediate strength of couplings between the lattices
a vertical cluster mean-field method is developed. This approximate approach
treats exactly particle dynamics during the vertical transitions between the
channels and it neglects the correlations along the channels. Our calculations
show that in all cases there are three stationary phases defined by particle
dynamics at entrances, at exits or in the bulk of the system, while phase
boundaries depend on the strength and symmetry of couplings between the
channels. Extensive Monte Carlo computer simulations strongly support our
theoretical predictions.Comment: 16 page
Frozen shuffle update for an asymmetric exclusion process on a ring
We introduce a new rule of motion for a totally asymmetric exclusion process
(TASEP) representing pedestrian traffic on a lattice. Its characteristic
feature is that the positions of the pedestrians, modeled as hard-core
particles, are updated in a fixed predefined order, determined by a phase
attached to each of them. We investigate this model analytically and by Monte
Carlo simulation on a one-dimensional lattice with periodic boundary
conditions. At a critical value of the particle density a transition occurs
from a phase with `free flow' to one with `jammed flow'. We are able to
analytically predict the current-density diagram for the infinite system and to
find the scaling function that describes the finite size rounding at the
transition point.Comment: 16 page
Open two-species exclusion processes with integrable boundaries
We give a complete classification of integrable Markovian boundary conditions
for the asymmetric simple exclusion process with two species (or classes) of
particles. Some of these boundary conditions lead to non-vanishing particle
currents for each species. We explain how the stationary state of all these
models can be expressed in a matrix product form, starting from two key
components, the Zamolodchikov-Faddeev and Ghoshal-Zamolodchikov relations. This
statement is illustrated by studying in detail a specific example, for which
the matrix Ansatz (involving 9 generators) is explicitly constructed and
physical observables (such as currents, densities) calculated.Comment: 19 pages; typos corrected, more details on the Matrix Ansatz algebr
Zero-range process with open boundaries
We calculate the exact stationary distribution of the one-dimensional
zero-range process with open boundaries for arbitrary bulk and boundary hopping
rates. When such a distribution exists, the steady state has no correlations
between sites and is uniquely characterized by a space-dependent fugacity which
is a function of the boundary rates and the hopping asymmetry. For strong
boundary drive the system has no stationary distribution. In systems which on a
ring geometry allow for a condensation transition, a condensate develops at one
or both boundary sites. On all other sites the particle distribution approaches
a product measure with the finite critical density \rho_c. In systems which do
not support condensation on a ring, strong boundary drive leads to a condensate
at the boundary. However, in this case the local particle density in the
interior exhibits a complex algebraic growth in time. We calculate the bulk and
boundary growth exponents as a function of the system parameters
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