Energy current cumulants in one-dimensional systems in equilibrium

TL;DR

This paper derives exact formulas for energy current cumulants in one-dimensional equilibrium systems using a connection to the KPZ equation, confirmed by simulations, revealing universal behaviors across different models.

Contribution

It introduces a method to compute exact energy current cumulants in 1D systems via KPZ correspondence, providing universal results and validation through simulations.

Findings

Exact cumulant generating function for energy current derived.

Universal results for cumulant combinations obtained.

Simulations confirm theoretical predictions.

Abstract

Recently a remarkable connection has been proposed between the fluctuating hydrodynamic equations of a one-dimensional fluid and the Kardar-Parizi-Zhang (KPZ) equation for interface growth. This connection has been used to relate equilibrium correlation functions of the fluid to KPZ correlation functions. Here we use this connection to compute the exact cumulant generating function for energy current in the fluid system. This leads to exact expressions for all cumulants and in particular to universal results for certain combinations of the cumulants. As examples, we consider two different systems which are expected to be in different universality classes, namely a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Simulations provide excellent confirmation of our theory.