Statistical properties of random banded matrices with strongly fluctuating diagonal elements
Abstract
Random banded matrices (RBM's) whose diagonal elements fluctuate more than the off-diagonal elements were introduced recently by Shepelyansky as a convenient means to model the coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using a mapping onto the same supersymmetric nonlinear σ model that was used earlier when considering 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 presented recently by Jacquod and Shepelyansky are reproduced by direct calculation of the distribution of eigenfunction components.
- Publication:
-
Physical Review B
- Pub Date:
- October 1995
- DOI:
- 10.1103/PhysRevB.52.R11580
- arXiv:
- arXiv:cond-mat/9507043
- Bibcode:
- 1995PhRvB..5211580F
- Keywords:
-
- 05.45.+b;
- 71.55.Jv;
- 72.15.Rn;
- Disordered structures;
- amorphous and glassy solids;
- Localization effects;
- Condensed Matter;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 7 pages,RevTex, no figures Submitted to Phys.Rev.B