Critical statistics in a power-law random banded matrix ensemble

Imre Varga; Daniel Braun

doi:10.1103/PhysRevB.61.R11859

Critical statistics in a power-law random banded matrix ensemble

Disordered Systems and Neural Networks 2009-10-31 v2 chao-dyn Mesoscale and Nanoscale Physics Chaotic Dynamics

Authors: 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 $H_{ij}\sim |i-j|^{-\mu}$ . 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'.

Keywords

random banded matrix critical statistics localization-delocalization transition multifractal spectral statistics weak chaos

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@article{arxiv.cond-mat/9909285,
  title  = {Critical statistics in a power-law random banded matrix ensemble},
  author = {Imre Varga and Daniel Braun},
  journal= {arXiv preprint arXiv:cond-mat/9909285},
  year   = {2009}
}

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4 pages in PS including 5 figures

Critical statistics in a power-law random banded matrix ensemble

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