Quantum dynamics and nonintegrability

Results of a nonperturbative investigation of the global behavior of quantum systems with time-periodic Hamiltonians are presented. These include the proof of a theorem stating that such systems, if bounded and nonresonant, will reassemble themselves infinitely often in the course of time. In order to illustrate the applicability of this result, an analytic study of a driven harmonic oscillator is presented, together with computer simulations of quantum maps describing the dynamics of a pulsed electron in a well and a periodically kicked rotor. A quantitative study of resonance excitation also shows that in practical situations recurrence is pervasive. Several unique quantum effects are analyzed, and their relevance to the classical limit is discussed. A formula is derived for recurrence times, and computer experiments are performed to test its validity.