Recent Developments in Energy Level Statistics in Generic Systems between Integrability and Chaos
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概要
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During the past decade or so there has been growing theoretical, numerical and experimental support for the Bohigas-Giannoni-Schmit Conjecture (1984) on the applicability of the random matrix theories statistics (GOE, GUE) in the classically ergodic quantal Hamiltonian systems. In the classically integrable systems the spectral fluctuations of the corresponding quantal Hamiltonians are well described by the Poissonian statistics. In the present paper we discuss the statistical properties of energy spectra of generic Hamiltonians in the transition region between integrability and ergodicity (KAM-systems). We present convincing statistically highly significant evidence for the fractional power law level repulsion (in the non-semiclassical limit, or near semiclassical limit), which is quite well fitted by the Brody distribution and even more so by the Izrailev distribution. However, at sufficiently large level spacings, say S>1, the Berry-Robnik formulae for the level spacing distribution are found to be adequate. We discuss the possible theoretical approaches and explanations. The phenomenon of power law level repulsion is partially understood in terms of the sparsed banded random matrix ensembles (SBRME).
- 理論物理学刊行会の論文
- 1994-08-12
著者
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Robnik Marko
Center For Applied Mathematics And Theoretical Physics University Of Maribor
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ROBNIK Marko
CAMTP Center for Applied Mathematics and Theoretical Physics, University of Maribor
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