Exact Non-Stationary Probabilities in the Asymmetric Exclusion Process on a Ring

TL;DR

This paper presents an exact, determinant-based solution for the non-stationary probabilities of particle configurations in the totally asymmetric exclusion process on a ring, advancing understanding of non-equilibrium statistical mechanics.

Contribution

It introduces a geometrical Bethe ansatz approach to derive explicit non-stationary probabilities for the ASEP on a ring, providing a new analytical tool.

Findings

Explicit determinant expression for non-stationary probabilities

Exact solution for particle configurations over time

Advances in analytical methods for ASEP

Abstract

By a geometrical treatment of the Bethe ansatz, we obtain an exact solution for the totally asymmetric exclusion process on a ring. We derive an explicit determinant expression for the non-stationary conditional probability $Prob(x_1,...,x_P;t|x_1^0,...,x_P^0;0)$ of finding $P$ particles on sites $x_1,...,x_P$ at time $t$ provided they are on sites $x_1^0,...,x_P^0$ at time $t=0$.