Quasiperiodically kicked quantum systems

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Abstract
We consider a two-state system kicked quasiperiodically by an external force. When the two kicking frequencies assumed for the force are incommensurate, there can be quantum chaos in the sense that (a) the autocorrelation function of the state vector decays, (b) the power spectrum of the state vector is broadband, and (c) the motion on the Bloch sphere is ergodic. The time evolution of the state vector is nevertheless dynamically stable in the sense that memory of the initial state is retained. We also consider briefly the kicked quantum rotator and find, in agreement with Shepelyansky [Physica 8D, 208 (1983)], that the quantum localization effect is greatly weakened by the presence of two incommensurate driving frequencies.

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