Dynamical Behavior of the Quantum Periodically Kicked Harmonic Oscillator
Zongfu Jiang · Communications in Theoretical Physics · 1993
We explore the properties of the quantum kicked harmonic oscillation governed by the Hamiltonian . The classical version of this model is known to exhibit certain type of stochastic behavior. We reduce the quantum equation of the model to quantum mapping equations. Numerical results of the mappings show that the behavior of the average energy as a function of time depends on the ration of the frequency of the external and that of the unperturbed system . The energy increases first very rapidly and then the energy growth saturates for irrational . The break time is independent of the strength of the external force, but is roughly proportional to . For a fixed rational the energy is damped oscillation for smaller T, and it is seemingly recurrent with time in the sense of Hogg and Huberman. In both cases, these behaviors of energy are independent of the strength of the external force and differ from the behavior of the quantum kicked rotator.