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Publication - Dr Martin Sieber

    Power-law random banded matrices and ultrametric matrices

    Eigenvector distribution in the intermediate regime

    Citation

    Bogomolny, E & Sieber, M, 2018, ‘Power-law random banded matrices and ultrametric matrices: Eigenvector distribution in the intermediate regime’. Physical Review E, vol 98.

    Abstract

    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 very well described by the generalised hyperbolic distribution which differs considerably from the usual Porter-Thomas distribution but shares with it certain universal properties.

    Full details in the University publications repository