Current fluctuations for totally asymmetric exclusion on the relaxation scale

TL;DR

This paper analyzes the current fluctuations in the one-dimensional totally asymmetric exclusion process during the relaxation scale, providing an exact calculation of the fluctuation distribution using Bethe ansatz in the thermodynamic limit.

Contribution

It introduces an exact method to compute current fluctuation distributions in ASEP during relaxation, linking them to scalar field realizations in a linear potential.

Findings

Exact Fourier transform of fluctuation distribution obtained

Distribution expressed as sum over scalar field realizations

Results valid in the thermodynamic limit with finite particle density

Abstract

The fluctuations of the current for the one-dimensional totally asymmetric exclusion process with $L$ sites are studied in the relaxation regime of times $T\sim L^{3/2}$. Using Bethe ansatz for the periodic system with an evolution conditioned on special initial and final states, the Fourier transform of the probability distribution of the fluctuations is calculated exactly in the thermodynamic limit $L\to\infty$ with finite density of particles. It is found to be equal to a sum over discrete realizations of a scalar field in a linear potential with coupling constant equal to the rescaled time $T/L^{3/2}$.