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Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime

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arxiv 1805.06675 v1 pith:ODQSPVF6 submitted 2018-05-17 math-ph math.MPquant-ph

E. Bogomolny , M. Sieber This is my paper · ORCID
classification math-phmath.MPquant-ph
keywords matricesdistributionrandombandedeigenvectormatrixpower-lawregime
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The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though in this case standard analytical tools are inapplicable, we found that in all considered cases eigenvector distributions are extremely well described by the generalised hyperbolic distribution which differs considerably from the usual Porter-Thomas distribution but shares with it certain universal properties.

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Cited by 1 Pith paper

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  1. How Random Are Ergodic Eigenstates of the Ultrametric Random Matrices and the Quantum Sun Model?

    quant-ph 2025-01 conditional novelty 5.0 of 10

    Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.

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