New Class of Random Matrix Ensembles with Multifractal Eigenvectors

Details New Class of Random Matrix Ensembles with Multifractal Eigenvectors New Class of Random Matrix Ensembles with Multifractal Eigenvectors

1997-03-18

arxiv.org/abs/cond-mat/9703167v2

Phys.Rev.Lett., 79 (1997) 1913.

Physics

Condensed Matter

4 pages RevTeX, resubmitted

Scientific paper

10.1103/PhysRevLett.79.1913

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three ensembles belong to a new class of critical RME with multifractal eigenfunction statistics and a universal critical spectral statitics. The generic form of the two-level correlation function for weak and extremely strong multifractality is suggested. Applications to the spectral statistics at the Anderson transition and for certain systems on the border of chaos and integrability is discussed.

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