Large-scale dispersive estimates for acoustic operators: homogenization meets localization

Fuente: arXiv
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Main Authors: Duerinckx, Mitia, Gloria, Antoine
Format: Preprint
Published: 2023
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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