Band edge localization and the density of states for acoustic and electromagnetic waves in random media

Citation
Jm. Combes et al., Band edge localization and the density of states for acoustic and electromagnetic waves in random media, ANN IHP-PHY, 70(4), 1999, pp. 381-428
Citations number
40
Categorie Soggetti
Physics
Journal title
ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE
ISSN journal
02460211 → ACNP
Volume
70
Issue
4
Year of publication
1999
Pages
381 - 428
Database
ISI
SICI code
0246-0211(199904)70:4<381:BELATD>2.0.ZU;2-Q
Abstract
The propagation of sound waves and electromagnetic radiation in a backgroun d medium is strongly influenced by the addition of random scatterers. We st udy random perturbations of a background medium which has a spectral gap in its permissible energy spectrum. We prove that the randomness localizes wa ves at energies near the band edges of the spectral gap of the background m edium. The perturbations of the dielectric function or the sound speed are described by Anderson-type potentials, which include random displacements f rom the equilibrium positions which model thermal vibrations. The waves wit h energies near the band edges are almost-surely exponentially localized. W e prove a Wegner estimate valid at all energies in the spectral gap of the unperturbed operator. It follows that the integrated density of states is L ipschitz continuous at energies in the unperturbed spectral gaps. (C) Elsev ier, Paris.