Exact solution of a one-parameter family of asymmetric exclusion processes

TL;DR

This paper introduces a family of asymmetric exclusion processes parameterized by λ, interpolating between known models, and provides an exact solution using the Bethe ansatz method.

Contribution

It defines a new one-parameter family of exclusion processes and derives their exact solutions, bridging different known models in the field.

Findings

Exact solutions for the family of processes across all λ values.

Demonstrates the interpolation between two well-known models.

Provides analytical tools for studying particle pushing dynamics.

Abstract

We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $\lambda \in [0,1] $, interpolating between the completely asymmetric processes [1] (for $\lambda =1$) and the n=1 drop-push models [2] (for $ \lambda =0$). For arbitrary $\la$, the model describes an exclusion process, in which a particle pushes its right neighbouring particles to the right, with rates depending on the number of these particles. Using the Bethe ansatz, we obtain the exact solution of the master equation .