Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles

doi:10.1088/1674-1056/abd92f

中国物理B ›› 2021, Vol. 30 ›› Issue (6): 60505-060505.doi: 10.1088/1674-1056/abd92f

Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles

Zhenjun Zhang(张振俊)^†, Jing Kang(康静), and Wen Wen(文文)

College of Science, Hohai University, Nanjing 210098, China

收稿日期:2020-11-28 修回日期:2020-12-31 接受日期:2021-01-07 出版日期:2021-05-18 发布日期:2021-06-17
通讯作者: Zhenjun Zhang E-mail:hi_zhangzhenjun@sina.com
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2017B17114 and B210202152).

Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles

Zhenjun Zhang(张振俊)^†, Jing Kang(康静), and Wen Wen(文文)

College of Science, Hohai University, Nanjing 210098, China

Received:2020-11-28 Revised:2020-12-31 Accepted:2021-01-07 Online:2021-05-18 Published:2021-06-17
Contact: Zhenjun Zhang E-mail:hi_zhangzhenjun@sina.com
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2017B17114 and B210202152).

摘要/Abstract

摘要： We study the behaviors of thermalization in Fermi-Pasta-Ulam-Tsingou (FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_eq depending on system's energy density ε scales as t_eq ∝ ε^-4 only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε^-4 will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.

关键词: FPUT system, thermalization, small number of particles

Abstract: We study the behaviors of thermalization in Fermi-Pasta-Ulam-Tsingou (FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_eq depending on system's energy density ε scales as t_eq ∝ ε^-4 only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε^-4 will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.

Key words: FPUT system, thermalization, small number of particles

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.60.Cd (Classical transport) 63.10.+a (General theory)

Zhenjun Zhang(张振俊), Jing Kang(康静), and Wen Wen(文文). Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles[J]. 中国物理B, 2021, 30(6): 60505-060505.

Zhenjun Zhang(张振俊), Jing Kang(康静), and Wen Wen(文文). Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles[J]. Chin. Phys. B, 2021, 30(6): 60505-060505.

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Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles

Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles

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