Critical statistics in a power-law random banded matrix ensemble

Details Critical statistics in a power-law random banded matrix ensemble Critical statistics in a power-law random banded matrix ensemble

1999-09-20

arxiv.org/abs/cond-mat/9909285v2

Phys. Rev. B61 RC 11859 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages in PS including 5 figures

Scientific paper

10.1103/PhysRevB.61.R11859

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'.

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