We study statistical properties of the ensemble of large N × N random matrices whose entries Hij decrease in a power-law fashion Hij ∼ |i − j|−α. Mapping the problem onto a nonlinear σ−model with… (More)

The explicit analytical expression for the distribution function of parametric derivatives of energy levels (”level velocities”) with respect to a random change of scattering potential is derived for… (More)

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… (More)