2,414 research outputs found
Spectral Statistics of the Two-Body Random Ensemble Revisited
Using longer spectra we re-analyze spectral properties of the two-body random
ensemble studied thirty years ago. At the center of the spectra the old results
are largely confirmed, and we show that the non-ergodicity is essentially due
to the variance of the lowest moments of the spectra. The longer spectra allow
to test and reach the limits of validity of French's correction for the number
variance. At the edge of the spectra we discuss the problems of unfolding in
more detail. With a Gaussian unfolding of each spectrum the nearest neighbour
spacing distribution between ground state and first exited state is shown to be
stable. Using such an unfolding the distribution tends toward a semi-Poisson
distribution for longer spectra. For comparison with the nuclear table ensemble
we could use such unfolding obtaining similar results as in the early papers,
but an ensemble with realistic splitting gives reasonable results if we just
normalize the spacings in accordance with the procedure used for the data.Comment: 11 pages, 7 figure
Universality for a class of random band matrices
We prove the universality for the eigenvalue gap statistics in the bulk of
the spectrum for band matrices, in the regime where the band width is
comparable with the dimension of the matrix, . All previous results
concerning universality of non-Gaussian random matrices are for mean-field
models. By relying on a new mean-field reduction technique, we deduce
universality from quantum unique ergodicity for band matrices
Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
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.Comment: Final version. 29 pages, 4 ps figures, uses iopart.st
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