Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

TL;DR

This paper provides an exact analysis of current fluctuations in the one-dimensional symmetric simple exclusion process with step initial conditions, revealing non-Gaussian behavior and growth of cumulants proportional to the square root of time.

Contribution

It introduces an exact calculation of current fluctuations for the symmetric simple exclusion process with step initial conditions using Bethe ansatz and Tracy-Widom identities.

Findings

Cumulants of current grow like √t.

Distribution decay is non-Gaussian with exp(-Q_t^3/t).

Results obtained via Bethe ansatz and Tracy-Widom identities.

Abstract

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line.