Tree structures for the current fluctuations in the exclusion process

TL;DR

This paper derives exact formulas for current fluctuations in an asymmetric exclusion process using tree structures, revealing three fluctuation regimes depending on system size and asymmetry scaling.

Contribution

It introduces a novel functional Bethe equation approach and tree-based expressions for cumulants in the asymmetric exclusion process.

Findings

Exact cumulant formulas involving tree structures

Identification of three fluctuation regimes

Dependence of fluctuation behavior on asymmetry scaling

Abstract

We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the model, we derive exact expressions for all the cumulants of the current in the stationary state. These expressions involve tree structures with composite nodes. In the thermodynamic limit, three regimes can be observed for the current fluctuations depending on how the asymmetry scales with the size of the system.