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Classical Random Matrix Ensembles

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Embedded Random Matrix Ensembles in Quantum Physics

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

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Abstract

Introduced first is the classification of the classical GOE, GUE and GSE ensembles. To get started with their properties, nearest neighbor spacing distributions (NNSD) for the simple 2×2 matrix version of these ensembles are derived. Going further, one and two-point functions (in the eigenvalues) for general N×N GOE and GUE are derived using the so called binary correlation approximation. Measures for level fluctuations as given by the number variance and Dyson-Mehta Δ 3 statistic on one hand and on the other strength functions, information entropy and Porter-Thomas distribution for wavefunction structure as generated by these ensembles are briefly discussed. In addition, presented are some aspects of data analysis.

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  1. Physical Research Laboratory, Ahmedabad, India

    V. K. B. Kota

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Kota, V.K.B. (2014). Classical Random Matrix 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_2

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