External field induced chaos in an infinite square well potential (Q1073412)

We study the motion of a particle in an infinite square well potential in the presence of a monochromatic external field. The equations of motion of this system have a particularly simple structure compared to other driven nonlinear systems, and yet the system exhibits a transition to chaotic behavior. The critical amplitudes of the external field where 'breakdown' of KAM invariants occurs and large scale chaos sets in are computed by numerical experiment. They are found to be in good agreement with predictions based on a renormalization group scheme.