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Dynamical energy equipartition of the Toda model with additional on-site potentials |
| Zhenjun Zhang(张振俊)1, Chunmei Tang(唐春梅)1, Jing Kang(康静)1, Peiqing Tong(童培庆)2,3 |
1. College of Science, Hohai University, Nanjing 210098, China;
2. School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China;
3. Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China |
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Abstract We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density ε and the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝ (1/ε)a(1/α)b, where b≈ 2a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.
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Received: 19 April 2017
Revised: 16 June 2017
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.60.Cd
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(Classical transport)
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63.10.+a
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(General theory)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11575087 and 11305045) and the Fundamental Research Funds for the Central Universities, China (Grant No. 2017B17114). |
Corresponding Authors:
Peiqing Tong
E-mail: pqtong@njnu.edu.cn
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Cite this article:
Zhenjun Zhang(张振俊), Chunmei Tang(唐春梅), Jing Kang(康静), Peiqing Tong(童培庆) Dynamical energy equipartition of the Toda model with additional on-site potentials 2017 Chin. Phys. B 26 100505
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