Analysis of a Kicked-Driven Model with a Modified Perturbation Potential

This investigation examines a kicked-driven model incorporating a distinct perturbation potential. The conventional kick rotor model describes a freely moving rotor subject to periodic perturbations in the form of a delta function potential applied at discrete time intervals. These perturbations can be realized in a cold atom system utilizing a pulsed laser field. Typically, the perturbation potential in this model is represented by cosine theta. However, this research employs a modified perturbation potential of cosine squared theta. Consequently, the Hamiltonian of the model is expressed as:

H(t) = (p^2 / 2m) + Kcos^2(theta) * sum(delta(t - nT)) from n = -infinity to +infinity

where K denotes the kick's intensity, and T represents the period of the delta function. This modified Hamiltonian provides a framework for analyzing the dynamics of the system under the influence of the altered perturbation potential.