Revisiting Multi-Wave Resonance in Classical Lattices: Quasi-Resonances, Not Exact Resonance, Govern Energy Redistribution

Wei Lin; Yong Zhang; Hong Zhao

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arXiv · 2507.05551

Revisiting Multi-Wave Resonance in Classical Lattices: Quasi-Resonances, Not Exact Resonance, Govern Energy Redistribution

Wei Lin·Yong Zhang·Hong Zhao

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Abstract

The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the multi-wave resonant kinetic equations possess distinctive symmetry properties that preferentially induce energy equalization between counter-propagating waves of identical frequency. This initial equalization disrupts the exact resonance condition, rendering it dynamically invalid. We further demonstrate that nonlinearity-mediated multi-wave quasi-resonances--not exact resonances--overn energy transfer and drive the system toward thermalization. Crucially, the strength of exact resonances decays with increasing system size, while quasi-resonance strength grows. Moreover, exact resonance strength remains independent of nonlinearity, whereas quasi-resonance strength diminishes with reduced nonlinearity. These observations provide additional evidence supporting the aforementioned conclusion while elucidating the size-dependent thermalization characteristics in lattice systems.

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Wei Lin, Yong Zhang, Hong Zhao. 2025-07-08. Revisiting Multi-Wave Resonance in Classical Lattices: Quasi-Resonances, Not Exact Resonance, Govern Energy Redistribution. https://arxiv.org/abs/2507.05551

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