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Preprint . 2011
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Integrable random matrix ensembles

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 14 Oct 2011Embargo end date: 01 Jan 2011Publisher:IOP PublishingJournal:Nonlinearity, volume 24, pages 3,179-3,213 (issn: 0951-7715, eissn: 1361-6544, Copyright policy )
Authors: Bogomolny, E.; Giraud, O.; Schmit, C.;

doi: 10.1088/0951-7715/24/11/010 , 10.48550/arxiv.1104.3777

arXiv: http://arxiv.org/abs/1104.3777

Integrable random matrix ensembles

Abstract

We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to integrability of the underlying system. Formulas for spacing distributions and level compressibility are obtained for various instances of such ensembles.

32 pages, 8 figures

Related Organizations
Keywords

Quantum Physics, [NLIN.NLIN-CD] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], FOS: Physical sciences, Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, Quantum Physics (quant-ph), [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
22
Top 10%
Top 10%
Average
Green
bronze