PMID: 11308555Apr 20, 2001Paper

Spectral statistics of the two-body random ensemble revisited

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
J FloresT H Seligman

Abstract

Using longer spectra we reanalyze spectral properties of the two-body random ensemble studied 30 years ago. At the center of the spectra the old results are largely confirmed, and we show that the nonergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spectra allow us 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-neighbor 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.

References

Jun 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·V V FlambaumF M Izrailev
Aug 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·V V FlambaumG Casati

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Citations

Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V V Flambaum, F M Izrailev
Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I Rotter
Dec 13, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Markus MüllerHiltrud Muhle
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lea F Santos, Marcos Rigol
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lea F Santos, Marcos Rigol
Aug 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Irving O MoralesA Frank
Sep 27, 2018·Physical Review. E·G Torres-VargasR Fossion
Apr 15, 2016·Physical Review. E·Rubem MondainiMarcos Rigol
Jan 9, 2021·Physical Review Letters·Michael WinerBrian Swingle
Aug 11, 2001·Physical Review Letters·M HoroiV Zelevinsky
Sep 13, 2002·Physical Review Letters·Philippe Jacquod, Imre Varga
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Markus MüllerHiltrud Muhle
Aug 25, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A RelañoJ Retamosa
Feb 28, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V K B Kota, K Kar

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