A general multi-wave quasi-resonance theory for lattice energy diffusion

TL;DR

This paper introduces a multi-wave quasi-resonance theory to analyze energy diffusion in classical lattices, revealing how eigenmode characteristics determine thermalization behavior and challenging traditional statistical mechanics assumptions.

Contribution

It develops a unified framework linking eigenmode properties to energy diffusion and thermalization, addressing the Fermi-Pasta-Ulam-Tsingou problem for large systems under weak perturbations.

Findings

Lattices with extended modes can be thermalized under weak perturbations.

Lattices without extended modes require stronger perturbations for thermalization.

Some lattices may inherently resist thermalization, violating statistical mechanics hypotheses.

Abstract

In this letter, a multi-wave quasi-resonance framework is established to analyze energy diffusion in classical lattices, uncovering that it is fundamentally determined by the characteristics of eigenmodes. Namely, based on the presence and the absence of extended modes, lattices fall into two universality classes with qualitatively different thermalization behavior. In particular, we find that while the one with extended modes can be thermalized under arbitrarily weak perturbations in the thermodynamic limit, the other class can be thermalized only when perturbations exceed a certain threshold, revealing for the first time the possibility that a lattice cannot be thermalized, violating the hypothesis of statistical mechanics. Our study addresses conclusively the renowned Fermi-Pasta-Ulam-Tsingou problem for large systems under weak perturbations, underscoring the pivotal roles of both extended and localized modes in facilitating energy diffusion and thermalization processes.