Abstract
The propagation of waves in disordered media is considered. Examples are provided by sound waves in materials of randomly varying composition or in turbulent fluids or electromagnetic waves in materials with randomly varying dielectric constant. The nature of the states at a given frequency is determined by studying the diffusion of the energy associated with the wave. In one and two dimensions diffusion vanishes at large distances leading to the conclusion that all states are localized. Above two dimensions a mobility edge in the diffusivity exists showing the existence of extended states at low frequencies and localized states at high frequencies. Phonon localization lengths are derived.
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© 1983 Springer-Verlag
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Stephen, M.J. (1983). Waves in disordered media. In: Hughes, B.D., Ninham, B.W. (eds) The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation. Lecture Notes in Mathematics, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073270
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DOI: https://doi.org/10.1007/BFb0073270
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