Exact Solution of the Master Equation for the Asymmetric Exclusion Process

TL;DR

This paper derives an exact solution for the master equation of the totally asymmetric exclusion process on an infinite 1D lattice using the Bethe ansatz, providing explicit probabilities for particle configurations over time.

Contribution

It presents the first exact solution of the master equation for this process, enabling precise analysis of particle dynamics.

Findings

Explicit expressions for conditional probabilities derived

Solution applicable to infinite lattice systems

Facilitates detailed study of asymmetric exclusion dynamics

Abstract

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P(x_1, ... ,x_N;t|y_1, ... ,y_N;0) of finding N particles on lattice sites x_1, ... ,x_N at time t with initial occupation y_1, ... ,y_N at time t=0.