Finite size scaling of current fluctuations in the totally asymmetric exclusion process

TL;DR

This paper investigates the fluctuations of current in the totally asymmetric exclusion process with open boundaries, revealing a first order phase transition in the cumulant generating function and analyzing finite size scaling using numerical methods.

Contribution

It introduces a numerical approach to study the cumulant generating function and identifies a first order space-time phase transition at s=0 in the model.

Findings

Identification of a first order phase transition at s=0

Finite size scaling behavior characterized near the transition

Numerical calculation of the cumulant generating function

Abstract

We study the fluctuations of the current J(t) of the totally asymmetric exclusion process with open boundaries. Using a density matrix renormalization group approach, we calculate the cumulant generating function of the current. This function can be interpreted as a free energy for an ensemble in which histories are weighted by exp(-sJ(t)). We show that in this ensemble the model has a first order space-time phase transition at s=0. We numerically determine the finite size scaling of the cumulant generating function near this phase transition, both in the non-equilibrium steady state and for large times.