A two--parametric family of asymmetric exclusion processes and its exact solution

TL;DR

This paper introduces a two-parameter family of asymmetric exclusion processes on a 1D lattice, exactly solvable via Bethe Ansatz, revealing how driving force and pushing influence system dynamics and steady states.

Contribution

It presents a novel exactly solvable model with two parameters controlling driving and pushing effects, expanding understanding of asymmetric exclusion processes.

Findings

Model is exactly solvable via coordinate Bethe Ansatz

N-particle S-matrix is factorizable

Interplay of driving and pushing affects steady states and dynamics

Abstract

A two--parameter family of asymmetric exclusion processes for particles on a one-dimensional lattice is defined. The two parameters of the model control the driving force and an effect which we call pushing, due to the fact that particles can push each other in this model. We show that this model is exactly solvable via the coordinate Bethe Ansatz and show that its {\it N}-particle $S$-matrix is factorizable. We also study the interplay of the above effects in determining various steady state and dynamical characteristics of the system.