3,159 research outputs found
Diffusion-limited annihilation in inhomogeneous environments
We study diffusion-limited (on-site) pair annihilation and
(on-site) fusion which we show to be equivalent for arbitrary
space-dependent diffusion and reaction rates. For one-dimensional lattices with
nearest neighbour hopping we find that in the limit of infinite reaction rate
the time-dependent -point density correlations for many-particle initial
states are determined by the correlation functions of a dual diffusion-limited
annihilation process with at most particles initially. By reformulating
general properties of annihilating random walks in one dimension in terms of
fermionic anticommutation relations we derive an exact representation for these
correlation functions in terms of conditional probabilities for a single
particle performing a random walk with dual hopping rates. This allows for the
exact and explicit calculation of a wide range of universal and non-universal
types of behaviour for the decay of the density and density correlations.Comment: 27 pages, Latex, to appear in Z. Phys.
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
Magnetophoresis of Tagged Polymers
We present quantitative results for the drift velocity of a polymer in a gel
if a force (e.g. through an electric or magnetic field) acts on a tag, attached
to one of its ends. This is done by introducing a modification of the
Rubinstein-Duke model for electrophoresis of DNA. We analyze this modified
model with exact and Monte Carlo calculations. Tagged magnetophoresis does not
show band collapse, a phenomenon that limits the applicability of traditional
electrophoresis to short polymers.Comment: 10 pages revtex, 3 PostScript figure
Bethe ansatz solution of zero-range process with nonuniform stationary state
The eigenfunctions and eigenvalues of the master-equation for zero range
process with totally asymmetric dynamics on a ring are found exactly using the
Bethe ansatz weighted with the stationary weights of particle configurations.
The Bethe ansatz applicability requires the rates of hopping of particles out
of a site to be the -numbers . This is a generalization of the rates
of hopping of noninteracting particles equal to the occupation number of a
site of departure. The noninteracting case can be restored in the limit . The limiting cases of the model for correspond to the totally
asymmetric exclusion process, and the drop-push model respectively. We analyze
the partition function of the model and apply the Bethe ansatz to evaluate the
generating function of the total distance travelled by particles at large time
in the scaling limit. In case of non-zero interaction, , the
generating function has the universal scaling form specific for the
Kardar-Parizi-Zhang universality class.Comment: 7 pages, Revtex4, mistypes correcte
Infinite reflections of shock fronts in driven diffusive systems with two species
Interaction of a domain wall with boundaries of a system is studied for a
class of stochastic driven particle models. Reflection maps are introduced for
the description of this process. We show that, generically, a domain wall
reflects infinitely many times from the boundaries before a stationary state
can be reached. This is in an evident contrast with one-species models where
the stationary density is attained after just one reflection.Comment: 11 pages, 8 eps figs, to appearin JPhysA 01.200
Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities
We study driven 1d lattice gas models with two types of particles and nearest
neighbor hopping. We find the most general case when there is a shock solution
with a product measure which has a density-profile of a step function for both
densities. The position of the shock performs a biased random walk. We
calculate the microscopic hopping rates of the shock. We also construct the
hydrodynamic limit of the model and solve the resulting hyperbolic system of
conservation laws. In case of open boundaries the selected steady state is
given in terms of the boundary densities.Comment: 12 pages, 4 figure
Quantum algebra symmetry of the ASEP with second-class particles
We consider a two-component asymmetric simple exclusion process (ASEP) on a
finite lattice with reflecting boundary conditions. For this process, which is
equivalent to the ASEP with second-class particles, we construct the
representation matrices of the quantum algebra that
commute with the generator. As a byproduct we prove reversibility and obtain in
explicit form the reversible measure. A review of the algebraic techniques used
in the proofs is given.Comment: 23 pages, presented at conference Particle systems and PDE's - III,
17-19 Dec 2014, Braga, Portuga
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
Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux
We consider the asymmetric simple exclusion processes (ASEP) on a ring
constrained to produce an atypically large flux, or an extreme activity. Using
quantum free fermion techniques we find the time-dependent conditional
transition probabilities and the exact dynamical structure factor under such
conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling
form. This gives a direct proof that the dynamical exponent in the extreme
current regime is rather than the KPZ exponent which
characterizes the ASEP in the regime of typical currents. Some of our results
extend to the activity in the partially asymmetric simple exclusion process,
including the symmetric case.Comment: 16 pages, 2 figure
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