Large-scale dispersive estimates for acoustic operators: homogenization meets localization
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910903727816704 |
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| author | Duerinckx, Mitia Gloria, Antoine |
| author_facet | Duerinckx, Mitia Gloria, Antoine |
| contents | This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive large-scale dispersive estimates for waves in disordered media that we apply to the spreading of low-energy eigenstates. This gives a short and direct proof that the lower spectrum of the acoustic operator is purely absolutely continuous in case of periodic media, and it further provides new lower bounds on the localization length of possible eigenstates in case of quasiperiodic or random media. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14046 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large-scale dispersive estimates for acoustic operators: homogenization meets localization Duerinckx, Mitia Gloria, Antoine Analysis of PDEs Mathematical Physics 82B44, 35B27, 35L05, 47B80, 60H25 This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive large-scale dispersive estimates for waves in disordered media that we apply to the spreading of low-energy eigenstates. This gives a short and direct proof that the lower spectrum of the acoustic operator is purely absolutely continuous in case of periodic media, and it further provides new lower bounds on the localization length of possible eigenstates in case of quasiperiodic or random media. |
| title | Large-scale dispersive estimates for acoustic operators: homogenization meets localization |
| topic | Analysis of PDEs Mathematical Physics 82B44, 35B27, 35L05, 47B80, 60H25 |
| url | https://arxiv.org/abs/2304.14046 |