Periodic Orbits in Fermi-Pasta-Ulam-Tsingou Systems
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| Format: | Preprint |
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2024
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| _version_ | 1866916424259207168 |
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| author | Karve, Nachiket Rose, Nathan Campbell, David |
| author_facet | Karve, Nachiket Rose, Nathan Campbell, David |
| contents | The FPUT paradox is the phenomenon whereby a one-dimensional chain of oscillators with nonlinear couplings shows non-ergodic behavior. The trajectory of the system in phase space, with a long wavelength initial condition, closely follows that of the Toda model over short times, as both systems seem to relax quickly to a non-thermal, metastable state. Over longer times, resonances in the FPUT spectrum drive the system towards equilibrium, away from the Toda trajectory. Similar resonances are observed in $q$-breather spectra, suggesting that $q$-breathers are involved in the route towards thermalization. In this article we investigate such resonances and show that they occur due to exact overlaps of $q$-breather frequencies of the type $mΩ_1 = Ω_k$. The resonances appear as peaks in the energy spectrum. Further, they give rise to new composite periodic orbits, which exist simultaneously with the original $q$-breathers. We find that such resonances are absent in integrable systems, as a consequence of the (infinite number of) conservation laws associated with integrability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_10790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic Orbits in Fermi-Pasta-Ulam-Tsingou Systems Karve, Nachiket Rose, Nathan Campbell, David Pattern Formation and Solitons The FPUT paradox is the phenomenon whereby a one-dimensional chain of oscillators with nonlinear couplings shows non-ergodic behavior. The trajectory of the system in phase space, with a long wavelength initial condition, closely follows that of the Toda model over short times, as both systems seem to relax quickly to a non-thermal, metastable state. Over longer times, resonances in the FPUT spectrum drive the system towards equilibrium, away from the Toda trajectory. Similar resonances are observed in $q$-breather spectra, suggesting that $q$-breathers are involved in the route towards thermalization. In this article we investigate such resonances and show that they occur due to exact overlaps of $q$-breather frequencies of the type $mΩ_1 = Ω_k$. The resonances appear as peaks in the energy spectrum. Further, they give rise to new composite periodic orbits, which exist simultaneously with the original $q$-breathers. We find that such resonances are absent in integrable systems, as a consequence of the (infinite number of) conservation laws associated with integrability. |
| title | Periodic Orbits in Fermi-Pasta-Ulam-Tsingou Systems |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2406.10790 |