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- W3009821581 abstract "Random Matrix Theory (RMT) has been a pivotal statistical technique in diverse disciplinesranging from nuclear spectroscopy to neural networking. The most prevalentuniversality classes in these systems are Wigner and Poisson ensembles. However, experimentaldata often show statistics intermediate between above symmetry classes. Inthis work, we have studied Rosenzweig-Porter Ensemble (RPE), which gives a naturalgeneralization of above ensembles, thus allowing to treat mixed dynamics as well. Herewe have observed some interesting phenomena, e.g. breaking of integrability in symmetricRPE and anti-unitary symmetry in hermitian RPE as rank of matrices is increased from 2to 3, existence of three different phases for rank 2 hermitian RPE etc. For small matriceswe have tried to obtain analytical expression, whereas for large ones, we have relied onnumerical data. We have produced some interpolating functions to quantify transitionfrom one behaviour to another. We have also studied some unconventional symmetrieslike centrosymmetry, persymmetry etc. Some interesting features are present in theseensembles, e.g. gradual breaking of integrability as thermodynamic limit is approached,oscillation of clustering strength as rank is increased, deviation of average Density of statesfrom Wigner's semicircle law, combination of two independent symmetries giving rise tolevel clustering despite the fact that both parent ensembles show level repulsion etc." @default.
- W3009821581 created "2020-03-13" @default.
- W3009821581 creator A5053789001 @default.
- W3009821581 creator A5064660585 @default.
- W3009821581 date "2019-05-01" @default.
- W3009821581 modified "2023-10-18" @default.
- W3009821581 title "Level Statistics forEnsembles of Random Matrices with Different Symmetry Properties" @default.
- W3009821581 hasPublicationYear "2019" @default.
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