Shocks in asymmetric simple exclusion processes of interacting particles

TL;DR

This paper investigates shock phenomena and phase transitions in asymmetric simple exclusion processes with particle interactions, analyzing how symmetry breaking and repulsive interactions influence particle current and density on open lattices.

Contribution

It introduces a detailed hydrodynamic analysis of shocks in ASEP with two types of interactions, extending understanding of non-equilibrium phase transitions in such systems.

Findings

Identification of shock formation due to symmetry breaking.

Analysis of current-density behavior near half filling.

Characterization of boundary layer effects in particle transport.

Abstract

In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest neighbor interactions. We consider two kinds of inter-particle interactions. In one case, the particle-hole symmetry is broken due to the interaction. In the other case, particles have an effective repulsion due to which the particle-current-density drops down near the half filling. These interacting particles move on a one dimensional lattice which is open at both the ends with injection of particles at one end and withdrawal of particles at the other. In addition to this, there are possibilities of attachments or detachments of particles to or from the lattice with certain rates. The hydrodynamic equation that involves the exact particle current-density of the particle conserving system and additional terms taking care of the attachment-detachment kinetics is studied using the techniques of boundary layer analysis.