Abstract
We introduce a dynamical system, for which it is possible to get such a large number of eigenvalues that deviations from Wigner's surmise are visible. The obtained level-spacing distribution agrees much better with the distribution derived from random matrix theory.
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TheN eigenvalues of the Floquet operator considered as functions of the kick strengthk are oscillating with a frequency proportional toj 3/2. Therefore, for a value of the angular momentumj=500 there are about 100 oscillations in ak interval of size 0.01. The spectra of the Floquet operator for values ofk differing by 0.01 can be considered as statistically independent
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Dietz, B., Zyczkowski, K. Level-spacing distributions beyond the Wigner surmise. Z. Physik B - Condensed Matter 84, 157–158 (1991). https://doi.org/10.1007/BF01453768
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DOI: https://doi.org/10.1007/BF01453768