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Classical lattices are classified into two thermalization universality classes based on eigenmode properties. Extended modes allow finite-time thermalization, while localized modes face potential inaccessibility with weak nonlinearity.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Understanding thermalization in classical lattices is crucial for statistical mechanics.
  • Previous studies have explored factors influencing thermalization, but a clear classification based on eigenmode properties was lacking.

Purpose of the Study:

  • To classify classical lattices into universality classes for thermalization.
  • To investigate the role of eigenmode properties in determining thermalization time and behavior.
  • To introduce and utilize a novel analytical tool for this classification.

Main Methods:

  • Systematic multiwave quasiresonance analysis was developed and applied.
  • Eigenmode properties (extended vs. localized) were analyzed.
  • Thermalization time and energy diffusion were studied as functions of nonlinearity strength and system size.

Main Results:

  • Two distinct universality classes for thermalization were identified based on eigenmode characteristics.
  • Lattices with extended modes thermalize in finite time, even with weak nonlinearity in large systems.
  • Lattices with localized modes exhibit complex scaling of thermalization time with decreasing nonlinearity, potentially hindering thermalization.

Conclusions:

  • Eigenmode properties are sufficient to classify classical lattices into two thermalization universality classes.
  • The findings provide a new framework for understanding thermalization dynamics in nonlinear lattice systems.
  • Qualitatively different energy diffusion behaviors were observed between the two identified classes.