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

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

2001-01-29

arxiv.org/abs/cond-mat/0101431v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure

Scientific paper

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 $\mu=1/2$ and the characteristic energy scale $\alpha$ is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential law $\propto e^{-\sqrt{\alpha t}}$. We analytically determine the localization length by a new method to derive the supersymmetric non-linear $\sigma$ model for this type of band matrices.

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