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          Institute: MPI für Kernphysik     Collection: Theory of Chaos, Fields and Statistical Inference     Display Documents

ID: 61253.0, MPI für Kernphysik / Theory of Chaos, Fields and Statistical Inference
Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons
Authors:Asaga, T.; Benet, L.; Rupp, T.; Weidenmüller, H.A.
Date of Publication (YYYY-MM-DD):2002
Title of Journal:Annals of Physics
Journal Abbrev.:Ann. Phys.
Start Page:229
End Page:249
Copyright:Copyright © 2002 Elsevier Science (USA). All rights reserved.
Review Status:Peer-review
Audience:Experts Only
Abstract / Description:We consider m spinless Bosons distributed over l degenerate single-particle states and interacting through a k-body random interaction with Gaussian probability distribution (the Bosonic embedded k-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as l goes against infiniti or as m goes adainst infiniti. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit l goes against infiniti the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as m goes against infiniti with both k and l fixed. Here we show that the ensemble is not ergodic and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency toward picket-fence-type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization.
External Publication Status:published
Document Type:Article
Affiliations:MPI für Kernphysik/Guest Groups and Emeriti/Theory (H.A. Weidenmüller)
External Affiliations:Laboratory of Physics, College of Science and Technology, Nihon University, 7-24-1 Narashino-dai, Funabashi, Chiba, Japan 274-8501
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