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Localization, Anomalous Diffusion, and Slow Relaxations: A Random Distance Matrix Approach

2010; American Physical Society; Volume: 105; Issue: 7 Linguagem: Inglês

10.1103/physrevlett.105.070601

1092-0145

Ariel Amir, Yuval Oreg, Y. Imry,

Material Dynamics and Properties

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum) and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.