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.
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Figotin, A., Klein, A. Localization of electromagnetic and acoustic waves in random media. Lattice models. J Stat Phys 76, 985–1003 (1994). https://doi.org/10.1007/BF02188695
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DOI: https://doi.org/10.1007/BF02188695