Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process

TL;DR

This paper provides an exact analytical confirmation of nonlinear fluctuating hydrodynamics predictions for a two-species exclusion process, revealing the joint current distribution and its long-term behavior.

Contribution

It derives exact formulas for the Green's function and joint current distribution, confirming hydrodynamics predictions for a multi-component system.

Findings

Limiting distribution is a product of Gaussian and GUE Tracy-Widom distributions.

First analytic confirmation of multi-component nonlinear fluctuating hydrodynamics.

Long-time behavior of current statistics matches theoretical predictions.

Abstract

We consider current statistics for a two species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of the model, and study its long time behavior. For a step type initial condition, we show that the limiting distribution is a product of the Gaussian and the GUE Tracy-Widom distribution. This is the first analytic confirmation for a multi-component system of a prediction from the recently proposed non-linear fluctuating hydrodynamics for one dimensional systems.