Localization and absence of Breit-Wigner form for Cauchy random band matrices

Klaus M. Frahm

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arXiv · cond-mat/0101431

Localization and absence of Breit-Wigner form for Cauchy random band matrices

Klaus M. Frahm

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Abstract

We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index $μ=1/2$ and the characteristic energy scale $α$ is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential law $\propto e^{-\sqrt{αt}}$. We analytically determine the localization length by a new method to derive the supersymmetric non-linear $σ$ model for this type of band matrices.

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Klaus M. Frahm. 2001-01-29. Localization and absence of Breit-Wigner form for Cauchy random band matrices. https://arxiv.org/abs/cond-mat/0101431

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