Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics

TL;DR

This paper investigates the dynamic correlations in classical anharmonic chains using nonlinear fluctuating hydrodynamics, providing analytical long-time asymptotics and numerical finite-time results for multi-mode systems.

Contribution

It extends fluctuating hydrodynamics to multi-mode systems and develops a mode-coupling framework with a quadratic memory kernel for these systems.

Findings

Analytical long-time asymptotics for correlators

Numerical simulation of mode-coupling equations

Generalization to other one-dimensional Hamiltonian systems

Abstract

We study the equilibrium time correlations for the conserved fields of classical anharmonic chains and argue that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics. In fact our scheme is more general and would cover also other one-dimensional hamiltonian systems, for example classical and quantum fluids. Fluctuating hydrodynamics is a nonlinear system of conservation laws with noise. For a single mode it is equivalent to the noisy Burgers equation, for which explicit solutions are available. Our focus is the case of several modes. No exact solutions have been found so far and we rely on a one-loop approximation. The resulting mode-coupling equations have a quadratic memory kernel and describe the time evolving 3 x 3 correlator matrix of the locally conserved fields. Long time asymptotics is computed analytically and finite time properties are obtained through a numerical simulation of the mode-coupling equations.