Thermalization without chaos in harmonic systems

TL;DR

This paper demonstrates that harmonic chains, despite being integrable and non-chaotic, can rapidly thermalize from certain initial conditions, challenging the notion that chaos is necessary for thermalization.

Contribution

It provides numerical evidence that harmonic systems can thermalize quickly without chaos, extending previous findings from the Toda model to the simplest integrable system.

Findings

Harmonic chains reach thermal equilibrium rapidly from atypical initial conditions.

Thermalization occurs regardless of the orthonormal basis used, if the initial state is random.

Chaos is not a prerequisite for thermalization in integrable systems.

Abstract

Recent numerical results showed that thermalization of Fourier modes is achieved in short time-scales in the Toda model, despite its integrability and the absence of chaos. Here we provide numerical evidence that the scenario according to which chaos is irrelevant for thermalization is realized even in the simplest of all classical integrable system: the harmonic chain. We study relaxation from an atypical condition given with respect to "random" modes, showing that a thermal state with equilibrium properties is attained in short times. Such a result is independent from the orthonormal base used to represent the chain state, provided it is random.