English

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

Condensed Matter 2009-10-28 v1 chao-dyn Chaotic Dynamics

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\sigma-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.

Keywords

Cite

@article{arxiv.cond-mat/9507043,
  title  = {Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements},
  author = {Yan V. Fyodorov and Alexander D. Mirlin},
  journal= {arXiv preprint arXiv:cond-mat/9507043},
  year   = {2009}
}

Comments

7 pages,RevTex, no figures Submitted to Phys.Rev.B

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