Relaxation of classical many-body hamiltonians in one dimension

TL;DR

This paper develops a mode-coupling theory to analyze how classical many-body Hamiltonian chains relax towards equilibrium, providing explicit estimates of relaxation times that align with previous numerical results and molecular dynamics simulations.

Contribution

It introduces a simple mode-coupling theoretical framework for one-dimensional Hamiltonian chains and compares its predictions with molecular dynamics data for the quartic Fermi-Pasta-Ulam potential.

Findings

Relaxation times depend on energy density and wavenumber.

Theoretical estimates agree with numerical simulations.

Qualitative interpretation of relaxation dynamics is achieved.

Abstract

The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wavenumber of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.