2,707 research outputs found
Totally asymmetric exclusion process with long-range hopping
Generalization of the one-dimensional totally asymmetric exclusion process
(TASEP) with open boundary conditions in which particles are allowed to jump
sites ahead with the probability is studied by
Monte Carlo simulations and the domain-wall approach. For the
standard TASEP phase diagram is recovered, but the density profiles near the
transition lines display new features when . At the first-order
transition line, the domain-wall is localized and phase separation is observed.
In the maximum-current phase the profile has an algebraic decay with a
-dependent exponent. Within the regime, where the
transitions are found to be absent, analytical results in the continuum
mean-field approximation are derived in the limit .Comment: 10 pages, 9 figure
Annihilating random walks in one-dimensional disordered media
We study diffusion-limited pair annihilation on one-dimensional
lattices with inhomogeneous nearest neighbour hopping in the limit of infinite
reaction rate. We obtain a simple exact expression for the particle
concentration of the many-particle system in terms of the
conditional probabilities for a single random walker in a dual
medium. For some disordered systems with an initially randomly filled lattice
this leads asymptotically to for the
disorder-averaged particle density. We also obtain interesting exact relations
for single-particle conditional probabilities in random media related by
duality, such as random-barrier and random-trap systems. For some specific
random barrier systems the Smoluchovsky approach to diffusion-limited
annihilation turns out to fail.Comment: LaTeX, 2 eps-figures, to be published in PR
Hydrodynamics of the zero-range process in the condensation regime
We argue that the coarse-grained dynamics of the zero-range process in the
condensation regime can be described by an extension of the standard
hydrodynamic equation obtained from Eulerian scaling even though the system is
not locally stationary. Our result is supported by Monte Carlo simulations.Comment: 14 pages, 3 figures. v2: Minor alteration
On the solvable multi-species reaction-diffusion processes
A family of one-dimensional multi-species reaction-diffusion processes on a
lattice is introduced. It is shown that these processes are exactly solvable,
provided a nonspectral matrix equation is satisfied. Some general remarks on
the solutions to this equation, and some special solutions are given. The
large-time behavior of the conditional probabilities of such systems are also
investigated.Comment: 13 pages, LaTeX2
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
Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes
Asymmetric exclusion processes for particles moving on parallel channels with
inhomogeneous coupling are investigated theoretically. Particles interact with
hard-core exclusion and move in the same direction on both lattices, while
transitions between the channels is allowed at one specific location in the
bulk of the system. An approximate theoretical approach that describes the
dynamics in the vertical link and horizontal lattice segments exactly but
neglects the correlation between the horizontal and vertical transport is
developed. It allows us to calculate stationary phase diagrams, particle
currents and densities for symmetric and asymmetric transitions between the
channels. It is shown that in the case of the symmetric coupling there are
three stationary phases, similarly to the case of single-channel totally
asymmetric exclusion processes with local inhomogeneity. However, the
asymmetric coupling between the lattices lead to a very complex phase diagram
with ten stationary-state regimes. Extensive Monte Carlo computer simulations
generally support theoretical predictions, although simulated stationary-state
properties slightly deviate from calculated in the mean-field approximation,
suggesting the importance of correlations in the system. Dynamic properties and
phase diagrams are discussed by analyzing constraints on the particle currents
across the channels
Exact solution of a one-parameter family of asymmetric exclusion processes
We define a family of asymmetric processes for particles on a one-dimensional
lattice, depending on a continuous parameter ,
interpolating between the completely asymmetric processes [1] (for ) and the n=1 drop-push models [2] (for ). For arbitrary \la,
the model describes an exclusion process, in which a particle pushes its right
neighbouring particles to the right, with rates depending on the number of
these particles. Using the Bethe ansatz, we obtain the exact solution of the
master equation .Comment: 14 pages, LaTe
EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS
Time-dependent correlation functions of (unstable) particles undergoing
biased or unbiased diffusion, coagulation and annihilation are calculated. This
is achieved by similarity transformations between different stochastic models
and between stochastic and soluble {\em non-stochastic} models. The results
agree with experiments on one-dimensional annihilation-coagulation processes.Comment: 15 pages, Latex. Some corrections made and an appendix adde
On Matrix Product States for Periodic Boundary Conditions
The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.Comment: 7 pages, late
Reaction fronts in stochastic exclusion models with three-site interactions
The microscopic structure and movement of reaction fronts in reaction
diffusion systems far from equilibrium are investigated. We show that some
three-site interaction models exhibit exact diffusive shock measures, i.e.
domains of different densities connected by a sharp wall without correlations.
In all cases fluctuating domains grow at the expense of ordered domains, the
absence of growth is possible between ordered domains. It is shown that these
models give rise to aspects not seen in nearest neighbor models, viz. double
shocks and additional symmetries. A classification of the systems by their
symmetries is given and the link of domain wall motion and a free fermion
description is discussed.Comment: 29 pages, 5 figure
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