Partially asymmetric exclusion models with quenched disorder

TL;DR

This paper investigates the dynamics of a one-dimensional asymmetric exclusion process with quenched disorder, deriving analytical expressions for the dynamical exponent using advanced statistical and renormalization techniques.

Contribution

It introduces an analytical method to calculate the dynamical exponent in disordered exclusion models, relating particlewise and sitewise disorder effects.

Findings

Derived z_{pt} for particlewise disorder

Established relation z_{st}=z_{pt}/2 for sitewise disorder

Identified ultra-slow diffusion in symmetric case

Abstract

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated distance traveled by the particles, x, scales with the time, t, as x ~ t^{1/z}, with a dynamical exponent z > 0. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method we analytically calculate, z_{pt}, for particlewise (pt) disorder, which is argued to be related to the dynamical exponent for sitewise (st) disorder as z_{st}=z_{pt}/2. In the symmetric situation with zero mean drift the particle diffusion is ultra-slow, logarithmic in time.