Localization, anomalous diffusion and slow relaxations: a random distance matrix approach

Ariel Amir; Yuval Oreg; Yoseph Imry

doi:10.1103/physrevlett.105.070601

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arXiv · 1002.2123

Localization, anomalous diffusion and slow relaxations: a random distance matrix approach

Ariel Amir·Yuval Oreg·Yoseph Imry

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Abstract

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.

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Ariel Amir, Yuval Oreg, Yoseph Imry. 2010-12-01. Localization, anomalous diffusion and slow relaxations: a random distance matrix approach. https://doi.org/10.1103/physrevlett.105.070601

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