Journal of Statistical Physics

, Volume 76, Issue 3–4, pp 985–1003 | Cite as

Localization of electromagnetic and acoustic waves in random media. Lattice models

  • Alexander Figotin
  • Abel Klein
Articles

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 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Alexander Figotin
    • 1
  • Abel Klein
    • 2
  1. 1.Department of MathematicsUniversity of North Carolina-CharlotteCharlotte
  2. 2.Department of MathematicsUniversity of California-IrvineIrvine

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