120 research outputs found
Large deviation functions in a system of diffusing particles with creation and annihilation
Large deviation functions for an exactly solvable lattice gas model of diffusing particles on a ring, subject to pair annihilation and creation, are obtained analytically using exact free-fermion techniques. Our findings for the large deviation function for the current are compared to recent results of Appert-Rolland et al. [Phys. Rev. E 78, 021122 (2008)] for diffusive systems with conserved particle number. Unlike conservative dynamics, our nonconservative model has no universal finite-size corrections for the cumulants. However, the leading Gaussian part has the same variance as in the conservative case. We also elucidate some properties of the large deviation functions associated with particle creation and annihilation
Unusual shock wave in two-species driven systems with an umbilic point
Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated
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.
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
Exact time-dependent correlation functions for the symmetric exclusion process with open boundary
As a simple model for single-file diffusion of hard core particles we
investigate the one-dimensional symmetric exclusion process. We consider an
open semi-infinite system where one end is coupled to an external reservoir of
constant density and which initially is in an non-equilibrium state
with bulk density . We calculate the exact time-dependent two-point
density correlation function and the mean and variance of the integrated average net flux
of particles that have entered (or left) the system up to time .
We find that the boundary region of the semi-infinite relaxing system is in a
state similar to the bulk state of a finite stationary system driven by a
boundary gradient. The symmetric exclusion model provides a rare example where
such behavior can be proved rigorously on the level of equal-time two-point
correlation functions. Some implications for the relaxational dynamics of
entangled polymers and for single-file diffusion in colloidal systems are
discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference
17 adde
Solution of a one-dimensional stochastic model with branching and coagulation reactions
We solve an one-dimensional stochastic model of interacting particles on a
chain. Particles can have branching and coagulation reactions, they can also
appear on an empty site and disappear spontaneously.
This model which can be viewed as an epidemic model and/or as a
generalization of the {\it voter} model, is treated analytically beyond the
{\it conventional} solvable situations. With help of a suitably chosen {\it
string function}, which is simply related to the density and the
non-instantaneous two-point correlation functions of the particles, exact
expressions of the density and of the non-instantaneous two-point correlation
functions, as well as the relaxation spectrum are obtained on a finite and
periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical
Review E (September 2001
Spectral Degeneracies in the Totally Asymmetric Exclusion Process
We study the spectrum of the Markov matrix of the totally asymmetric
exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY
filling. Although the system does not possess obvious symmetries except
translation invariance, the spectrum presents many multiplets with degeneracies
of high order. This behaviour is explained by a hidden symmetry property of the
Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the
corresponding number of multiplets are derived and compared with numerical
results obtained from exact diagonalisation of small size systems. This
unexpected structure of the TASEP spectrum suggests the existence of an
underlying large invariance group.
Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur
DMRG studies of the effect of constraint release on the viscosity of polymer melts
The scaling of the viscosity of polymer melts is investigated with regard to
the molecular weight. We present a generalization of the Rubinstein-Duke model,
which takes constraint releases into account and calculate the effects on the
viscosity by the use of the Density Matrix Renormalization Group (DMRG)
algorithm. Using input from Rouse theory the rates for the constraint release
are determined in a self consistent way. We conclude that shape fluctuations of
the tube caused by constraint release are not a likely candidate for improving
Doi's crossover theory for the scaling of the polymer viscosity.Comment: 6 pages, 8 figure
Current moments of 1D ASEP by duality
We consider the exponential moments of integrated currents of 1D asymmetric
simple exclusion process using the duality found by Sch\"utz. For the ASEP on
the infinite lattice we show that the th moment is reduced to the problem of
the ASEP with less than or equal to particles.Comment: 13 pages, no figur
Determinant representation for some transition probabilities in the TASEP with second class particles
We study the transition probabilities for the totally asymmetric simple
exclusion process (TASEP) on the infinite integer lattice with a finite, but
arbitrary number of first and second class particles. Using the Bethe ansatz we
present an explicit expression of these quantities in terms of the Bethe wave
function. In a next step it is proved rigorously that this expression can be
written in a compact determinantal form for the case where the order of the
first and second class particles does not change in time. An independent
geometrical approach provides insight into these results and enables us to
generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde
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