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Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

Yan V. Fyodorov·Alexander D. Mirlin
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Abstract

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $σ-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.

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Yan V. Fyodorov, Alexander D. Mirlin. 1995-07-13. Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements. https://doi.org/10.1103/physrevb.52.r11580

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