Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain

TL;DR

This paper tests a nonlinear hydrodynamic fluctuation theory for Fermi-Pasta-Ulam chains through molecular dynamics simulations, confirming many theoretical predictions about sound and heat mode behaviors with some observed deviations.

Contribution

It provides the first numerical validation of the nonlinear hydrodynamic fluctuation theory for anharmonic oscillator chains, specifically Fermi-Pasta-Ulam models.

Findings

Good agreement with KPZ and Levy-walk scaling predictions

Some deviations observed in correlation functions

Supports the validity of the nonlinear hydrodynamic theory

Abstract

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correlations satisfies Levy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We find very good agreement in many cases, but also some deviations.