Statistical analysis of composite spectra

We consider nearest-neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of such data. One problem lies in fitting the nearest-neighbor...

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Bibliographic Details
Published in:Annals of physics 2006-03, Vol.321 (3), p.560-580
Main Authors: Abul-Magd, A.Y., Harney, H.L., Simbel, M.H., Weidenmüller, H.A.
Format: Article
Language:English
Subjects:
Chaos
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CORRELATIONS
INFORMATION THEORY
Short level sequences
SPATIAL DISTRIBUTION
SPECTRA
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Summary:We consider nearest-neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of such data. One problem lies in fitting the nearest-neighbor spacing distribution to the histogram of level spacings obtained from the data. We show that the method of Bayesian inference is superior to this procedure. The second problem occurs when one unfolds such short sequences. We show that the unfolding procedure generically leads to an overestimate of the chaoticity parameter. This trend is absent in the presence of long-range level correlations. Thus, composite ensembles of levels from a system with long-range spectral stiffness yield reliable information about the chaotic behavior of the system.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2005.04.005