Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

✍ Scribed by L. Benet; T. Rupp; H.A. Weidenmüller

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 194 KB
• Volume: 292
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2001.6156

✦ Synopsis

We consider m spinless Fermions in l > m degenerate single-particle levels interacting via a kbody random interaction with Gaussian probability distribution and k ≤ m in the limit l → ∞ (the embedded k-body random ensembles). We address the cases of orthogonal and unitary symmetry. We derive a novel eigenvalue expansion for the second moment of the Hilbert-space matrix elements of these ensembles. Using properties of the expansion and the supersymmetry technique, we show that for 2k > m, the average spectrum has the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson type. Using a generalization of the binary correlation approximation, we show that for k m l, the spectral fluctuations are Poissonian. This is consistent with the case k = 1 which can be solved explicitly. We construct limiting ensembles which are either fully integrable or fully chaotic and show that the k-body random ensembles lie between these two extremes. Combining all these results we find that the spectral correlations for the embedded ensembles gradually change from Wigner-Dyson for 2k > m to Poissonian for k m l.