On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators

TL;DR

This paper investigates how a chain of anharmonic oscillators approaches equilibrium, suggesting large systems always relax without an ergodicity threshold, but the relaxation time diverges as anharmonicity decreases.

Contribution

It provides new insights into the relaxation behavior of anharmonic oscillator chains, indicating no ergodicity threshold and analyzing the divergence of relaxation time.

Findings

Large systems relax to equilibrium distribution

No ergodicity threshold observed

Relaxation time diverges as anharmonicity approaches zero

Abstract

In this note we study the approach to equilibrium of a chain of anharmonic oscillators. We find indications that a sufficiently large system always relaxes to the usual equilibrium distribution. There is no sign of an ergodicity threshold. The time however to arrive to equilibrium diverges when $g \to 0$, $g$ being the anharmonicity.