Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates

TL;DR

This paper applies the Bethe ansatz to derive exact determinant formulas for the conditional probabilities and current distribution in a TASEP model with particle-dependent hopping rates, providing precise analytical results.

Contribution

It introduces a novel exact solution for TASEP with particle-dependent rates using Bethe ansatz, extending previous models with uniform rates.

Findings

Exact determinant formulas for conditional probabilities

Explicit expression for the time-integrated current

Analytical insights into particle-dependent TASEP dynamics

Abstract

Using the Bethe ansatz we obtain in a determinant form the exact solution of the master equation for the conditional probabilities of the totally asymmetric exclusion process with particle-dependent hopping rates on Z. From this we derive a determinant expression for the time-integrated current for a step-function initial state.