Localized Mode and Nonergodicity of a Harmonic Oscillator Chain

TL;DR

This paper introduces a simple model of coupled harmonic oscillators that exhibits nonergodic behavior due to localized modes, despite the nonergodicity strength vanishing, revealing new insights into ergodicity breaking.

Contribution

The study demonstrates that localized modes can cause nonergodicity in harmonic oscillator chains, challenging traditional indicators like nonergodicity strength.

Findings

Velocity autocorrelation function oscillates asymptotically.

Localized mode with isolated frequency causes nonergodicity.

Model analyzed via molecular dynamics and exact diagonalization.

Abstract

We present a simple and microscopic physical model that breaks the ergodicity. Our model consists of coupled classical harmonic oscillators, and the motion of the tagged particle obeys the generalized Langevin equation satisfying the second fluctuation dissipation theorem. It is found that although the nonergodicity strength, which is expected to detect the ergodicity breaking, for this model vanishes, the velocity auto correlation function of the tagged particle asymptotically oscillates. We analyze the model by using the molecular dynamics and the exact diagonalization as well as the rigorous mapping to the generalized Langevin equation. Our analysis reveals that the asymptotic oscillation is caused by a localized mode with an isolated frequency from the continuous phonon spectrum.