Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2022-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ac8ac3 |
| _version_ | 1797748352678363136 |
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| author | Liangtao Peng Weicheng Fu Yong Zhang Hong Zhao |
| author_facet | Liangtao Peng Weicheng Fu Yong Zhang Hong Zhao |
| author_sort | Liangtao Peng |
| collection | DOAJ |
| description | Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the N /2 mode in both the Fermi–Pasta–Ulam–Tsingou- α and - β chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time T as a function of the perturbation strength λ follows the same behavior; i.e., $T\propto {(\lambda -{\lambda }_{\mathrm{c}})}^{-\frac{1}{2}}$ , where λ _c is the instability threshold. The dependence of λ _c on N is also obtained. The results of T and λ _c agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed. |
| first_indexed | 2024-03-12T16:03:30Z |
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| id | doaj.art-4b77c1605ed04f7c8ee4c1d7ba3a772b |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:03:30Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
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| series | New Journal of Physics |
| spelling | doaj.art-4b77c1605ed04f7c8ee4c1d7ba3a772b2023-08-09T14:26:59ZengIOP PublishingNew Journal of Physics1367-26302022-01-0124909300310.1088/1367-2630/ac8ac3Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chainsLiangtao Peng0https://orcid.org/0000-0002-2102-674XWeicheng Fu1https://orcid.org/0000-0002-5420-7985Yong Zhang2https://orcid.org/0000-0001-5808-7936Hong Zhao3https://orcid.org/0000-0001-7667-1386Department of Physics, Xiamen University , Xiamen 361005, Fujian, People’s Republic of ChinaDepartment of Physics, Tianshui Normal University , Tianshui 741001, Gansu, People’s Republic of China; Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University , Lanzhou 730000, Gansu, People’s Republic of ChinaDepartment of Physics, Xiamen University , Xiamen 361005, Fujian, People’s Republic of China; Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University , Lanzhou 730000, Gansu, People’s Republic of ChinaDepartment of Physics, Xiamen University , Xiamen 361005, Fujian, People’s Republic of China; Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University , Lanzhou 730000, Gansu, People’s Republic of ChinaNonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the N /2 mode in both the Fermi–Pasta–Ulam–Tsingou- α and - β chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time T as a function of the perturbation strength λ follows the same behavior; i.e., $T\propto {(\lambda -{\lambda }_{\mathrm{c}})}^{-\frac{1}{2}}$ , where λ _c is the instability threshold. The dependence of λ _c on N is also obtained. The results of T and λ _c agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed.https://doi.org/10.1088/1367-2630/ac8ac3Fermi–Pasta–Ulam–Tsingou chainsnonlinear normal modesinstability dynamicsFloquet theory |
| spellingShingle | Liangtao Peng Weicheng Fu Yong Zhang Hong Zhao Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains New Journal of Physics Fermi–Pasta–Ulam–Tsingou chains nonlinear normal modes instability dynamics Floquet theory |
| title | Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains |
| title_full | Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains |
| title_fullStr | Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains |
| title_full_unstemmed | Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains |
| title_short | Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains |
| title_sort | instability dynamics of nonlinear normal modes in the fermi pasta ulam tsingou chains |
| topic | Fermi–Pasta–Ulam–Tsingou chains nonlinear normal modes instability dynamics Floquet theory |
| url | https://doi.org/10.1088/1367-2630/ac8ac3 |
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