A Note on Quantum Chaology and Gamma Approximations to Eigenvalue Spacings for Infinite Random Matrices

Quantum counterparts of certain classical systems exhibit chaotic spectral statistics of their energy levels; eigenvalues of infinite random matrices model irregular spectra. Eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real symmetric matrices admit a gamma distr...

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Bibliographic Details
Published inTopics On Chaotic Systems pp. 96 - 103
Main Author Dodson, C. T. J.
Format Book Chapter
LanguageEnglish
Published WORLD SCIENTIFIC 01.05.2009
Subjects
Random matrices
gamma distribution
information geometry
GUE
eigenvalue spacing
GSE
randomness
GOE
quantum chaotic
statistics
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Summary:Quantum counterparts of certain classical systems exhibit chaotic spectral statistics of their energy levels; eigenvalues of infinite random matrices model irregular spectra. Eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real symmetric matrices admit a gamma distribution approximation, as do the hermitian unitary (GUE) and quaternionic symplectic (GSE) cases. Then chaotic and non-chaotic cases fit in the information geometric framework of the manifold of gamma distributions, which has been the subject of recent work on neighbourhoods of randomness for general stochastic systems.
ISBN:9789814468237
9814468231
9789814271332
9789814271349
9814271330
9814271349
DOI:10.1142/9789814271349_0011