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We analyze the effects of a nonlinear cubic perturbation on the delta-KickedRotor. We consider two different models, in which the nonlinear term actseither in the position or in the momentum representation. We numericallyinvestigate the modifications induced by the nonlinearity in the quantumtransport in both localized and resonant regimes and a comparison between theresults for the two models is presented. Analyzing the momentum distributionsand the increase of the mean square momentum, we find that the quantumresonances asymptotically are very stable with respect to the nonlinearperturbation of the rotor's phase evolution. For an intermittent time regime,the nonlinearity even enhances the resonant quantum transport, leading tosuperballistic motion.Comment: 8 pages, 10 figures; to appear in Phys. Rev.

Delocalized and resonant quantum transport in nonlinear generalizations of the kicked rotor model