Critical statistics in a power-law random banded matrix ensemble

Abstract

We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j{|}^{-\mu }$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the parameter $\mu$. The model is critical at $\mu =1$ and the eigenstates are multifractals. Based on numerical simulations we demonstrate that the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be a general feature of systems exhibiting a LDT or `weak chaos'.

4 pages in PS including 5 figures

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