Partially Asymmetric Exclusion Processes with Sitewise Disorder

Abstract

We study the stationary properties as well as the non-stationary dynamics of the one-dimensional partially asymmetric exclusion process with position dependent random hop rates. In a finite system of $L$ sites the stationary current, $J$, is determined by the largest barrier and the corresponding waiting time, $\tau \sim J^{-1}$, is related to the waiting time of a single random walker, ${\tau }_{rw}$, as $\tau \sim {\tau }_{rw}^{1/2}$. The current is found to vanish as: $J\sim L^{-z/2}$, where $z$ is the dynamical exponent of the biased single particle Sinai walk. Typical stationary states are phase separated: At the largest barrier almost all particles queue at one side and almost all holes are at the other side. The high-density (low-density) region, is divided into $\sim L^{1/2}$ connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study non-stationary processes of the system, like coarsening and invasion. Finally we discuss some related models, where particles of larger size or multiple occupation of lattice sites is considered.

11 pages, 11 figures

References in corpus (3)

• Driven Diffusive Systems with Disorder
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

Cited by in corpus (25)

• Renormalization group study of the two-dimensional random transverse-field Ising model
• Phase diagram and edge effects in the ASEP with bottlenecks
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Totally asymmetric exclusion process with site-wise dynamic disorder
• Defect-induced phase transition in the asymmetric simple exclusion process
• Large deviations, condensation, and giant response in a statistical system
• Disordered driven lattice gases with boundary reservoirs and Langmuir kinetics
• Dynamics at barriers in bidirectional two-lane exclusion processes
• Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space
• Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State
• Random elastic networks : strong disorder renormalization approach
• Development and regression of a large fluctuation
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach
• Non-equilibrium dynamics of finite-dimensional disordered systems : RG flow towards an "infinite disorder" fixed point at large times
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model
• Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder
• Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder
• A Biologically Motivated Asymmetric Exclusion Process: interplay of congestion in RNA polymerase traffic and slippage of nascent transcript
• Anomalous transport in disordered exclusion processes with coupled particles
• Mean field treatment of exclusion processes with random-force disorder
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process
• Symmetry Breaking of Current Response in Disordered Exclusion Processes