Regular and chaotic quantum dynamics in the driven square well

The quantum dynamics of the periodically-driven infinite square well is examined. This simple system illustrates some important aspects of quantum chaos. The phase space structure of the quantum eigenstates are shown to mimic the structure of the classical phase space and these eigenstates show a transition from “regular” to “chaotic” as the strength of the driving field is increased. The spacing of eigenvalues undergoes a transition from Poisson to COE statistics as the classical system becomes chaotic. High-harmonic generation in the radiation spectrum is shown to be closely tied to the onset of chaos in the classical system.