Thermalization of two- and three-dimensional classical lattices

Abstract

Whether and how a system reaches thermalization is a fundamental issue of statistical physics. While for one-dimensional lattices this issue has been intensively studied in terms of energy equipartition for more than half a century, few work has been performed in the case of two- and three-dimensional lattices, and thus the thermalization dynamics remains unclear for more realistic lattices. In this Letter we investigate analytically and numerically the time-scaling of energy relaxation in these lattices. We show that the equipartition of energy is generally reached following a universal scheme for large enough lattices, regardless of its dimensionality, its specific lattice structure, and whether the system is translation invariant or not. Our results have practical significance in exploring the effect of high-order nonlinearities, i.e., the combining effect of multi-phonon process, in solid materials.

5 pages, 3 figures

References in corpus (3)

• Heat Transport in low-dimensional systems
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Universal law of thermalization for one-dimensional perturbed Toda lattices

Cited by in corpus (7)

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• A general multi-wave quasi-resonance theory for lattice energy diffusion
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• Thermalization in asymmetric harmonic chains
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• Further exploration of the machine-learning-based nuclear mass table