Searching for the Tracy-Widom distribution in nonequilibrium processes

TL;DR

This paper investigates the presence of Tracy-Widom distribution in nonequilibrium one-dimensional systems, specifically in a Fermi-Pasta-Ulam chain, revealing that current fluctuations follow this distribution under certain conditions.

Contribution

It demonstrates that in a nonequilibrium anharmonic chain, the time-integrated current exhibits Tracy-Widom distributed fluctuations, extending its known applications beyond growth processes.

Findings

Time-integrated current has a linear deterministic component.

Fluctuations scale as t^{1/3} and follow Tracy-Widom distribution.

Validates Tracy-Widom distribution's role in nonequilibrium transport phenomena.

Abstract

While originally discovered in the context of the Gaussian Unitary Ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters the profile develops a rarefaction wave, while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam type anharmonic chain we will demonstrate that the time-integrated current has a deterministic contribution, linear in time $t$, and fluctuations of size $t^{1/3}$ with a Tracy-Widom distributed random amplitude.