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Interpolating and Other Extended Classical Ensembles

  • Chapter
Embedded Random Matrix Ensembles in Quantum Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 884))

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Abstract

Changes in the nature of level fluctuations in the situations such as (i) a symmetry is gradually broken, (ii) two good symmetry subspaces are gradually admixed, (iii) ordered (integrable) spectra gradually become chaotic and so on are studied by using interpolating and/or partitioned random matrix ensembles. Results are presented for: (i) Poisson to GOE and GUE and GOE to GUE transitions using 2×2 matrix version of these interpolations; (ii) Rosenzweig-Porter ensemble for superposition of good symmetry subspaces; (iii) 2×2 partitioned GOE; (iv) a GOE related covariance random matrix ensemble. Applications of these ensembles in physics are emphasized with particular reference to nuclear structure data. In addition, further extensions and applications of RMT are listed. Results in this and the previous chapter are used to define various statistical quantities, notations and so on that are needed for easy reading of the remaining chapters of this book.

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    V. K. B. Kota

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Kota, V.K.B. (2014). Interpolating and Other Extended Classical Ensembles. In: Embedded Random Matrix Ensembles in Quantum Physics. Lecture Notes in Physics, vol 884. Springer, Cham. https://doi.org/10.1007/978-3-319-04567-2_3

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