2,022 research outputs found
Solution of a class of one-dimensional reaction-diffusion models in disordered media
We study a one-dimensional class of reaction-diffusion models on a
parameters manifold. The equations of motion of the correlation
functions close on this manifold. We compute exactly the long-time behaviour of
the density and correlation functions for
{\it quenched} disordered systems. The {\it quenched} disorder consists of
disconnected domains of reaction. We first consider the case where the disorder
comprizes a superposition, with different probabilistic weights, of finite
segments, with {\it periodic boundary conditions}. We then pass to the case of
finite segments with {\it open boundary conditions}: we solve the ordered
dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and
investigate further its disordered version.Comment: 11 pages, no figures. To appear in Phys.Rev.
The asymmetric exclusion model with sequential update
We present a solution for the stationary state of an asymmetric exclusion
model with sequential update and open boundary conditions. We solve the model
exactly for random hopping in both directions by applying a matrix-product
formalism which was recently used to solve the model with sublattice-parallel
update[1]. It is shown that the matrix-algebra describing the sequential update
and sublattice-parallel update are identical and can be mapped onto the random
sequential case treated by Derrida et al[2].Comment: 7 pages, Late
On U_q(SU(2))-symmetric Driven Diffusion
We study analytically a model where particles with a hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asymmetric
hopping rates. The system dynamics are given by the
\mbox{U[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic
Heisenberg antiferromagnet. Exploiting this symmetry we derive exact
expressions for various correlation functions. We discuss the density profile
and the two-point function and compute the correlation length as well
as the correlation time . The dynamics of the density and the
correlations are shown to be governed by the energy gaps of a one-particle
system. For large systems and depend only on the asymmetry. For
small asymmetry one finds indicating a dynamical exponent
as for symmetric diffusion.Comment: 10 pages, LATE
Finite-size effects on the dynamics of the zero-range process
We study finite-size effects on the dynamics of a one-dimensional zero-range
process which shows a phase transition from a low-density disordered phase to a
high-density condensed phase. The current fluctuations in the steady state show
striking differences in the two phases. In the disordered phase, the variance
of the integrated current shows damped oscillations in time due to the motion
of fluctuations around the ring as a dissipating kinematic wave. In the
condensed phase, this wave cannot propagate through the condensate, and the
dynamics is dominated by the long-time relocation of the condensate from site
to site.Comment: 5 pages, 5 figures, version published in Phys. Rev. E Rapid
Communication
The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation
In this paper we address the relationship between zero temperature Glauber
dynamics and the diffusion-annihilation problem in the free fermion case. We
show that the well-known duality transformation between the two problems can be
formulated as a similarity transformation if one uses appropriate (toroidal)
boundary conditions. This allow us to establish and clarify the precise nature
of the relationship between the two models. In this way we obtain a one-to-one
correspondence between observables and initial states in the two problems. A
random initial state in Glauber dynamics is related to a short range correlated
state in the annihilation problem. In particular the long-time behaviour of the
density in this state is seen to depend on the initial conditions. Hence, we
show that the presence of correlations in the initial state determine the
dependence of the long time behaviour of the density on the initial conditions,
even if such correlations are short-ranged. We also apply a field-theoretical
method to the calculation of multi-time correlation functions in this initial
state.Comment: 15 pages, Latex file, no figures. To be published in J. Phys. A.
Minor changes were made to the previous version to conform with the referee's
Repor
Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
We consider a discrete-time random walk where the random increment at time
step depends on the full history of the process. We calculate exactly the
mean and variance of the position and discuss its dependence on the initial
condition and on the memory parameter . At a critical value
where memory effects vanish there is a transition from a weakly localized
regime (where the walker returns to its starting point) to an escape regime.
Inside the escape regime there is a second critical value where the random walk
becomes superdiffusive. The probability distribution is shown to be governed by
a non-Markovian Fokker-Planck equation with hopping rates that depend both on
time and on the starting position of the walk. On large scales the memory
organizes itself into an effective harmonic oscillator potential for the random
walker with a time-dependent spring constant . The solution of
this problem is a Gaussian distribution with time-dependent mean and variance
which both depend on the initiation of the process.Comment: 10 page
Landau functions for non-interacting bosons
We discuss the statistics of Bose-Einstein condensation (BEC) in a canonical
ensemble of N non-interacting bosons in terms of a Landau function L_N^{BEC}
(q) defined by the logarithm of the probability distribution of the order
parameter q for BEC. We also discuss the corresponding Landau function for
spontaneous symmetry breaking (SSB), which for finite N should be distinguished
from L_N^{BEC}. Only for intinite N BEC and SSB can be described by the same
Landau function which depends on the dimensionality and on the form of the
external potential in a surprisingly complex manner. For bosons confined by a
three-dimensional harmonic trap the Landau function exhibits the usual behavior
expected for continuous phase transitions.Comment: 4 pages, 4 figures; final version to appear as a rapid communication
in Physical Review A. Abstract modified and typos correcte
Monte Carlo simulations of bosonic reaction-diffusion systems
An efficient Monte Carlo simulation method for bosonic reaction-diffusion
systems which are mainly used in the renormalization group (RG) study is
proposed. Using this method, one dimensional bosonic single species
annihilation model is studied and, in turn, the results are compared with RG
calculations. The numerical data are consistent with RG predictions. As a
second application, a bosonic variant of the pair contact process with
diffusion (PCPD) is simulated and shown to share the critical behavior with the
PCPD. The invariance under the Galilean transformation of this boson model is
also checked and discussion about the invariance in conjunction with other
models are in order.Comment: Publishe
Steady State and Dynamics of Driven Diffusive Systems with Quenched Disorder
We study the effect of quenched disorder on nonequilibrium systems of
interacting particles, specifically, driven diffusive lattice gases with
spatially disordered jump rates. The exact steady-state measure is found for a
class of models evolving by drop-push dynamics, allowing several physical
quantities to be calculated. Dynamical correlations are studied numerically in
one dimension. We conjecture that the relevance of quenched disorder depends
crucially upon the speed of the kinematic waves in the system. Time-dependent
correlation functions, which monitor the dissipation of kinematic waves, behave
as in pure system if the wave speed is non-zero. When the wave speed vanishes,
e.g. for the disordered exclusion process close to half filling, disorder is
strongly relevant and induces separation of phases with different macroscopic
densities. In this case the exponent characterizing the dynamical correlation
function changes.Comment: 4 pages, RevTeX, 4 eps figures included using 'psfig.sty
Non-universal dynamics of dimer growing interfaces
A finite temperature version of body-centered solid-on-solid growth models
involving attachment and detachment of dimers is discussed in 1+1 dimensions.
The dynamic exponent of the growing interface is studied numerically via the
spectrum gap of the underlying evolution operator. The finite size scaling of
the latter is found to be affected by a standard surface tension term on which
the growth rates depend. This non-universal aspect is also corroborated by the
growth behavior observed in large scale simulations. By contrast, the
roughening exponent remains robust over wide temperature ranges.Comment: 11 pages, 7 figures. v2 with some slight correction
- …