Abstract
A transformation on the two-dimensional torus which is related to the problem of limit distribution for the distance between the levels in the kicked-rotator model is considered. The first four moments of the r.w. which describe the numbers of visits of a point in a rectangle of measure ε are calculated. It is shown that when ε→0 they converge to the first four moments of a Poisson r.w.
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References
G. Casati, I. Guarneri, F. M. Izrailev, “Statistical properties of the quasi-energy spectrum of a simple integrable system.” Preprint 87-31, Novosibirsk, USSR.
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Pellegrinotti, A. Evidence for the poisson distribution for quasi-energies in the quantum kicked-rotator model. J Stat Phys 53, 1327–1336 (1988). https://doi.org/10.1007/BF01023872
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DOI: https://doi.org/10.1007/BF01023872