Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds
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| Format: | Preprint |
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2023
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| _version_ | 1866909446970540032 |
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| author | De Roeck, Wojciech Huveneers, François Prośniak, Oskar A. |
| author_facet | De Roeck, Wojciech Huveneers, François Prośniak, Oskar A. |
| contents | We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter $λ$, and on the other hand our numerics show that it follows a power law for a broad range of values of $λ$. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10572 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds De Roeck, Wojciech Huveneers, François Prośniak, Oskar A. Statistical Mechanics Disordered Systems and Neural Networks We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter $λ$, and on the other hand our numerics show that it follows a power law for a broad range of values of $λ$. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems. |
| title | Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2308.10572 |