Statistics of quasi-energy separations in chaotic systems.

Abstract

summary, this work confirms that the quasi-energy nearest-neighbor spacings distribution of the kicked rotor is Poissonian and therefore is similar to the corresponding dis-tribution for energy levels spacing in the one-dimensional localization problem. This is further evidence for the simi-larity between these two problems. This distribution is very different from the ones that were obtained so far for sto-chastic problems with time-independent Hamiltonians. Therelevant difference between the quantal behavior of these two classes of problems, both chaotic in their classical limit,is the extension or localization of the wave functions. Note added. After submission of this paper we learned of work by F. M. Israilev (unpublished, in Russian) which isfully consistent with ours, although the emphasis is quite different. We thank M. V. Berry for communicating thiswork to us.We thank H. G. Schuster for suggestions and encourage-ment at carly stages of this work and M. V. Berry for com-ments