2,671 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
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
Entangling power of permutation invariant quantum states
We investigate the von Neumann entanglement entropy as function of the size
of a subsystem for permutation invariant ground states in models with finite
number of states per site, e.g., in quantum spin models. We demonstrate that
the entanglement entropy of sites in a system of length generically
grows as , where is the on-site spin
and is a function depending only on magnetization.Comment: 6 pages, 2 figure
Phase Coexistence in Driven One Dimensional Transport
We study a one-dimensional totally asymmetric exclusion process with random
particle attachments and detachments in the bulk. The resulting dynamics leads
to unexpected stationary regimes for large but finite systems. Such regimes are
characterized by a phase coexistence of low and high density regions separated
by domain walls. We use a mean-field approach to interpret the numerical
results obtained by Monte-Carlo simulations and we predict the phase diagram of
this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let
Non-equilibrium tube length fluctuations of entangled polymers
We investigate the nonequilibrium tube length fluctuations during the
relaxation of an initially stretched, entangled polymer chain. The
time-dependent variance of the tube length follows in the early-time
regime a simple universal power law originating in the
diffusive motion of the polymer segments. The amplitude is calculated
analytically both from standard reptation theory and from an exactly solvable
lattice gas model for reptation and its dependence on the initial and
equilibrium tube length respectively is discussed. The non-universality
suggests the measurement of the fluctuations (e.g. using flourescence
microscopy) as a test for reptation models.Comment: 12 pages, 2 figures. Minor typos correcte
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
Non-equilibrium Dynamics of Finite Interfaces
We present an exact solution to an interface model representing the dynamics
of a domain wall in a two-phase Ising system. The model is microscopically
motivated, yet we find that in the scaling regime our results are consistent
with those obtained previously from a phenomenological, coarse-grained Langevin
approach.Comment: 12 pages LATEX (figures available on request), Oxford preprint
OUTP-94-07
The statistics of diffusive flux
We calculate the explicit probability distribution function for the flux
between sites in a simple discrete time diffusive system composed of
independent random walkers. We highlight some of the features of the
distribution and we discuss its relation to the local instantaneous entropy
production in the system. Our results are applicable both to equilibrium and
non-equilibrium steady states as well as for certain time dependent situations.Comment: 12 pages, 1 figur
Shocks in the asymmetric exclusion process with internal degree of freedom
We determine all families of Markovian three-states lattice gases with pair
interaction and a single local conservation law. One such family of models is
an asymmetric exclusion process where particles exist in two different
nonconserved states. We derive conditions on the transition rates between the
two states such that the shock has a particularly simple structure with minimal
intrinsic shock width and random walk dynamics. We calculate the drift velocity
and diffusion coefficient of the shock.Comment: 26 pages, 1 figur
Diffusion-Annihilation in the Presence of a Driving Field
We study the effect of an external driving force on a simple stochastic
reaction-diffusion system in one dimension. In our model each lattice site may
be occupied by at most one particle. These particles hop with rates
to the right and left nearest neighbouring site resp. if this
site is vacant and annihilate with rate 1 if it is occupied. We show that
density fluctuations (i.e. the moments of the
density distribution at time ) do not depend on the spatial anisotropy
induced by the driving field, irrespective of the initial condition.
Furthermore we show that if one takes certain translationally invariant
averages over initial states (e.g. random initial conditions) even local
fluctuations do not depend on . In the scaling regime the
effect of the driving can be completely absorbed in a Galilei transformation
(for any initial condition). We compute the probability of finding a system of
sites in its stationary state at time if it was fully occupied at time
.Comment: 17 pages, latex, no figure
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