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Universal scaling of the thermalization time in one-dimensional lattices

Weicheng Fu, Yong Zhang, and Hong Zhao
Phys. Rev. E 100, 010101(R) – Published 15 July 2019
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Abstract

We show that, in the thermodynamic limit, a one-dimensional (1D) nonlinear lattice can always be thermalized for arbitrarily small nonlinearity, thus proving the equipartition theorem for a class of systems. Particularly, we find that in the lattices with nearest-neighbor interaction potential V(x)=x2/2+λxn/n with n4, the thermalization time, Teq, follows a universal scaling law; i.e., Teqλ2ε(n2), where ε is the energy per particle. Numerical simulations confirm that it is accurate for an even n, while a certain degree of deviation occurs for an odd n, which is attributed to the extra vibration modes excited by the asymmetric interaction potential. This finding suggests that although the symmetry of interactions will not affect the system reaching equipartition eventually, it affects the process toward equipartition. Based on the scaling law found here, a unified formula for the thermalization time of a 1D general nonlinear lattice is obtained.

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  • Received 23 December 2018
  • Revised 20 May 2019

DOI:https://doi.org/10.1103/PhysRevE.100.010101

©2019 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsCondensed Matter, Materials & Applied PhysicsFluid DynamicsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Weicheng Fu, Yong Zhang, and Hong Zhao*

  • Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, Fujian, China

  • *zhaoh@xmu.edu.cn

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Issue

Vol. 100, Iss. 1 — July 2019

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