Exact Resonances Are Not Sufficient for Phonon Energy Diffusion

Abstract:Multi-phonon resonance conditions underpin kinetic theories of phonon transport and lattice thermalization. We show that exact resonance matching, nonzero interaction coefficients, and network connectivity do not guarantee persistent energy diffusion. Symmetry-enforced balance relations drive exact-resonant collision currents to nonthermal zero-flux states, producing kinetic arrest from individual resonant sets to connected networks. Complete energy spreading is sustained by quasi-resonances. The thermodynamic and weak-nonlinearity limits do not commute: the leading kinetic behavior is recovered in the former, whereas at fixed finite size the thermalization time diverges through higher-order crossovers as the nonlinearity vanishes. Exact-resonance existence and connectivity are therefore kinematic, not sufficient dynamical, criteria for phonon energy diffusion.

Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Classical Physics (physics.class-ph); Quantum Physics (quant-ph)

arXiv:2608.03180 [cond-mat.stat-mech]

(or arXiv:2608.03180v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2608.03180 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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