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

Eugene Bogomolny, Martin Sieber

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)
284 Downloads (Pure)

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.
Original languageEnglish
Article number042116
Number of pages8
JournalPhysical Review E
Volume98
Issue number4
Early online date8 Oct 2018
DOIs
Publication statusPublished - Oct 2018

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