Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries

TL;DR

This paper computes the first four cumulants of the current in a one-dimensional symmetric exclusion process with open boundaries, revealing universal distribution features similar to quantum conductors.

Contribution

It provides explicit formulas for the first four cumulants of the current and conjectures a universal form for all higher cumulants based on these results.

Findings

Explicit expressions for the first four cumulants of the current.

A conjecture predicting all higher cumulants.

Universal distribution matching quantum conductor results.

Abstract

We calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of $N$ sites with open boundary conditions. For large system size $N$, the generating function of the integrated current depends on the densities $\rho_a$ and $\rho_b$ of the two reservoirs and on the fugacity $z$, the parameter conjugated to the integrated current, through a single parameter. Based on our expressions for these first four cumulants, we make a conjecture which leads to a prediction for all the higher cumulants. In the case $\rho_a=1$ and $\rho_b=0$, our conjecture gives the same universal distribution as the one obtained by Lee, Levitov and Yakovets for one dimensional quantum conductors in the metallic regime.