Abstract
We analyse a scheme of transition from the Poissonian statistics for quantum levels to the Gaussian one of random matrix ensembles in the framework of level dynamics discussed by Yukawa. We propose a means of connecting these two limiting statistics by showing a result that Yukawa's parameter γ/β of the exponential family can be efficiently replaced by the ratio <E>/<Q> which reflects directly a degree of the eigenvalue correlations of each sample matrix in the ensemble. On this basis, we discuss a correspondence between the level statistics of a generic quantum system and its classical regular/chaotic dynamics in terms of the semiclassical power spectrum and its second moment formulated by Feingold-Peres and Prosen-Robnik. We also discuss some limiting procedures N→∞ (infinite limit of the matrix dimension) pertinent to the Gaussian ensembles, and remark about the possibility of fractional power law of Brody's type.
Original language | English (US) |
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Pages (from-to) | 529-535 |
Number of pages | 7 |
Journal | Zeitschrift für Physik B Condensed Matter |
Volume | 93 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1994 |
Keywords
- 03.65
- 05.40
- 05.45
ASJC Scopus subject areas
- Condensed Matter Physics