arXiv subjects

F. H. Jafarpour

Publications and source records attributed to F. H. Jafarpour.

9 recordsLinked to original sources

arXiv2016

Enantiodromic effective generators of a Markov jump process with Gallavotti-Cohen symmetry

This paper deals with the properties of the stochastic generators of the effective (driven) processes associated with atypical values of transition-dependent time-integrated currents with Gallavotti-Cohen symmetry in Markov jump processes. Exploiting the concept of biased ensemble of trajectories by introducing a biasing field $s$, we show that the stochastic generators of the effective processes associated with the biasing fields $s$ and $E-s$ are enantiodromic with respect to each other where $E$ is the conjugated field to the current. We illustrate our findings by considering an exactly solvable creation-annihilation process of classical particles with nearest-neighbor interactions defined on a one-dimensional lattice.

cond-mat.stat-mech↗

arXiv2014

Particle current fluctuations in a variant of asymmetric Glauber model

We study the total particle current fluctuations in a one-dimensional stochastic system of classical particles consisting of branching and death processes which is a variant of asymmetric zero-temperature Glauber dynamics. The full spectrum of a modified Hamiltonian, whose minimum eigenvalue generates the large deviation function for the total particle current fluctuations through a Legendre-Fenchel transformation, is obtained analytically. Three examples are presented and numerically exact results are compared to our analytical calculations.

cond-mat.stat-mech↗

arXiv2012

Relaxation time in a non-conserving driven-diffusive system with parallel dynamics

We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.

cond-mat.stat-mech↗

arXiv2011

A heterogeneous zero-range process related to a two-dimensional walk model

We have considered a disordered driven-diffusive system defined on a ring. This system can be mapped onto a heterogeneous zero-range process. We have shown that the grand-canonical partition function of this process can be obtained using a matrix product formalism and that it is exactly equal to the partition function of a two-dimensional walk model. The canonical partition function of this process is also calculated. Two simple examples are presented in order to confirm the results.

cond-mat.stat-mech↗

arXiv2009

Temporal evolution of product shock measures in TASEP with sublattice-parallel update

It is known that when the steady state of a one-dimensional multispecies system, which evolves via a random-sequential updating mechanism, is written in terms of a linear combination of Bernoulli shock measures with random-walk dynamics, it can be equivalently expressed as a matrix-product state. In this case the quadratic algebra of the system always has a two-dimensional matrix representation. Our investigations show that this equivalence exists at least for the systems with deterministic sublattice-parallel update. In this paper we consider the totally asymmetric simple exclusion process on a finite lattice with open boundaries and sublattice-parallel update as an example.

cond-mat.stat-mech↗

arXiv2008

Repelling Random Walkers in a Diffusion-Coalescence System

We have shown that the steady state probability distribution function of a diffusion-coalescence system on a one-dimensional lattice of length L with reflecting boundaries can be written in terms of a superposition of double shock structures which perform biased random walks on the lattice while repelling each other. The shocks can enter into the system and leave it from the boundaries. Depending on the microscopic reaction rates, the system is known to have two different phases. We have found that the mean distance between the shock positions is of order L in one phase while it is of order 1 in the other phase.

cond-mat.stat-mech↗

arXiv2007

A Family of Exactly-Solvable Driven-Diffusive Systems in One-dimension

We introduce an exactly-solvable family of one-dimensional driven-diffusive systems defined on a discrete lattice. We find the quadratic algebra of this family which has an infinite-dimensional representation. We discuss the phase diagram of the system in a couple of special cases.

cond-mat.stat-mech↗

arXiv2004

Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation

We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two different phases which are separated by a second-order phase transition. The thermodynamic behavior of the canonical partition function of the model has been calculated exactly in each phase. Density profiles of particles have also been obtained explicitly. It is shown that the exponential part of the density profiles decay on three different length scales which depend on total density of particles.

cond-mat.stat-mech↗

arXiv2003

Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems

We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the partially asymmetric exclusion process with open boundaries, (ii) of a lattice Fisher wave in a reaction-diffusion system, and (iii) of a domain wall in non-equilibrium Glauber-Kawasaki dynamics with magnetization current. For each of these systems we define a microscopic shock position and calculate the exact hopping rates of the travelling wave in terms of the transition rates of the microscopic model. In the steady state a reversal of the bias of the travelling wave marks a first-order non-equilibrium phase transition, analogous to the Zel'dovich theory of kinetics of first-order transitions. The stationary distributions of the exclusion process with $n$ shocks can be described in terms of $n$-dimensional representations of matrix product states.

cond-mat.stat-mech↗