Long persistence of localization in a disordered anharmonic chain beyond the atomic limit
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910769880236032 |
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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 establish rigorous bounds on the decorrelation time and thermal transport in the disordered Klein-Gordon chain with a quartic on-site potential, governed by a parameter $λ$. At $λ= 0$, the chain is harmonic, and any form of transport is fully suppressed by Anderson localization. For the anharmonic system, at $λ> 0$, our results show that decorrelation and transport can occur only on time scales that grow faster than any polynomial in $1/λ$ as $λ\to 0$. From a technical perspective, the main novelty of our work is that we don't restrict ourselves to the atomic limit. Instead, we develop perturbation theory around the harmonic system with a fixed harmonic interaction between nearby oscillators. This allows us to compare our mathematical results with previous numerical work and contribute to resolving an ongoing debate, as detailed in a companion paper arXiv:2308.10572. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11243 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long persistence of localization in a disordered anharmonic chain beyond the atomic limit De Roeck, Wojciech Huveneers, François Prośniak, Oskar A. Mathematical Physics We establish rigorous bounds on the decorrelation time and thermal transport in the disordered Klein-Gordon chain with a quartic on-site potential, governed by a parameter $λ$. At $λ= 0$, the chain is harmonic, and any form of transport is fully suppressed by Anderson localization. For the anharmonic system, at $λ> 0$, our results show that decorrelation and transport can occur only on time scales that grow faster than any polynomial in $1/λ$ as $λ\to 0$. From a technical perspective, the main novelty of our work is that we don't restrict ourselves to the atomic limit. Instead, we develop perturbation theory around the harmonic system with a fixed harmonic interaction between nearby oscillators. This allows us to compare our mathematical results with previous numerical work and contribute to resolving an ongoing debate, as detailed in a companion paper arXiv:2308.10572. |
| title | Long persistence of localization in a disordered anharmonic chain beyond the atomic limit |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2308.11243 |