A family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice

TL;DR

This paper introduces a new family of exactly-solvable discrete-time exclusion processes on a one-dimensional lattice, unifying several models and providing explicit probability calculations using Bethe-ansatz.

Contribution

It presents a two-parameter family of discrete-time exclusion processes, extending continuous-time models and deriving explicit solutions via boundary conditions and Bethe-ansatz.

Findings

Contains the asymmetric simple exclusion process as a special case

Calculates conditional probabilities explicitly

Determines drift and diffusion rates for two particles

Abstract

A two-parameter family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice is introduced, which contains the asymmetric simple exclusion process and the drop-push model as particular cases. The process is rewritten in terms of boundary conditions, and the conditional probabilities are calculated using the Bethe-ansatz. This is the discrete-time version of the continuous-time processes already investigated in [1-3]. The drift- and diffusion-rates of the particles are also calculated for the two-particle sector.