Localization of Electromagnetic and Acoustic Waves in Random Media. Lattice Models (1994)
| Venue: | Lattice Model, J. Stat. Phys |
| Citations: | 11 - 4 self |
BibTeX
@ARTICLE{Figotin94localizationof,
author = {Alexander Figotin and Abel Klein},
title = {Localization of Electromagnetic and Acoustic Waves in Random Media. Lattice Models},
journal = {Lattice Model, J. Stat. Phys},
year = {1994},
volume = {76},
pages = {985--1003}
}
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Abstract
We consider lattice versions of Maxwell's equations and of the equation that governs the propagation of acoustic waves in a random medium. The vector nature of electromagnetic waves is fully taken into account. The medium is assumed to be a small perturbation of a periodic one. We prove rigorously that localized eigenstates arise in a vicinity of the edges of the gaps in the spectrum. A key ingredient is a new Wegner-type estimate for a class of lattice operators with off-diagonal disorder. Key words: localization, random media, electromagnetic waves, acoustic waves, lattice model. The work is supported by U. S. Air Force grant AFOSR-91-0243 y The work is partially supported by NSF grant DMS 9208029 1 Introduction Decades after P. W. Anderson [1] described the remarkable phenomenon of the localization in space of electron wave functions in disordered solids, physicists have begun to ask whether other waves, say electromagnetic or acoustic, can be localized if the propagating m...
