Review of the k-Body Embedded Ensembles of Gaussian Random Matrices

Details Review of the k-Body Embedded Ensembles of Gaussian Random Matrices Review of the k-Body Embedded Ensembles of Gaussian Random Matrices

2002-07-26

arxiv.org/abs/cond-mat/0207656v2

J.Phys.A36:3569-3594,2003

Physics

Condensed Matter

Final version. 29 pages, 4 ps figures, uses iopart.sty

Scientific paper

10.1088/0305-4470/36/12/340

The embedded ensembles were introduced by Mon and French as physically more plausible stochastic models of many--body systems governed by one--and two--body interactions than provided by standard random--matrix theory. We review several approaches aimed at determining the spectral density, the spectral fluctuation properties, and the ergodic properties of these ensembles: moments methods, numerical simulations, the replica trick, the eigenvector decomposition of the matrix of second moments and supersymmetry, the binary correlation approximation, and the study of correlations between matrix elements.

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