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arXiv · cond-mat/9909285

Critical statistics in a power-law random banded matrix ensemble

Imre Varga·Daniel Braun
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Abstract

We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-μ}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the parameter $μ$. The model is critical at $μ=1$ 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'.

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Imre Varga, Daniel Braun. 2000-02-24. Critical statistics in a power-law random banded matrix ensemble. https://doi.org/10.1103/physrevb.61.r11859

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