Diluted banded random matrices: scaling behavior of eigenfunction and spectral properties

Abstract

We demonstrate that the normalized localization length β of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law . The scaling parameter of the model is defined as , where is the average number of non-zero elements per matrix row, N is the matrix size, and . Additionally, we show that also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues.