Revisiting Multi-Wave Resonance in Classical Lattices: Quasi-Resonances, Not Exact Resonance, Govern Energy Redistribution
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911044760240128 |
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| author | Lin, Wei Zhang, Yong Zhao, Hong |
| author_facet | Lin, Wei Zhang, Yong Zhao, Hong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_05551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Multi-Wave Resonance in Classical Lattices: Quasi-Resonances, Not Exact Resonance, Govern Energy Redistribution Lin, Wei Zhang, Yong Zhao, Hong Statistical Mechanics Chaotic Dynamics Classical Physics 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. |
| title | Revisiting Multi-Wave Resonance in Classical Lattices: Quasi-Resonances, Not Exact Resonance, Govern Energy Redistribution |
| topic | Statistical Mechanics Chaotic Dynamics Classical Physics |
| url | https://arxiv.org/abs/2507.05551 |