Jamming and condensation in one-dimensional driven flow

TL;DR

This paper investigates how jamming and condensation phenomena interact in a modified one-dimensional driven flow model, revealing conditions under which local defects become irrelevant and how condensation suppresses jamming.

Contribution

It introduces a modified TASEP model incorporating interaction-dependent hopping rates and analyzes the interplay of jamming and condensation using mean-field theory and numerical checks.

Findings

Condensation of holes can suppress particle jamming.

Partially-condensed phase emerges as a key state.

Modified model shows phase diagram with new behaviors.

Abstract

We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially-condensed phase is the most interesting, compared to that in the original SB problem.