 There is an interesting physical model of a charged particle in a unit square with periodic boundary conditions with an external electromagnetic field that occasionally gives it a kick (turns on and off). Mathematically this model is a generalization of the quantized Arnold cat map (Arnold and Avez 1968; Weigert 1990; Weigert 1993). Physically it represents a charged particle confined to an energy surface shaped like a torus that receives kicks from an external field. The classical model has trajectories that exhibit the stretching and folding process that seems to be a necessary condition for chaos, has positive Lyapunov exponents, and is algorithmically complex[12], one of the measures used to detect classical chaos. Its trajectories have many of the marks of chaos. For the quantum model, the kick of the electromagnetic field has the effect of mapping the quantum labels of state vectors that are initially close together to labels which do not necessarily ever come close again. This is somewhat reminiscent of the divergence of classical chaotic trajectories except that it is the change in the state labels that plays the role of the classical trajectories. This leads to an absolutely continuous quasi-energy spectrum (the quasi-energy is defined as the set of numbers representing the “energy” in the evolution operator acting on state vector labels). The expectation value of the particle position becomes unpredictable with respect to the initial state label after long times and one can show that the sequence of shifts of the quantum state labels is algorithmically complex. Moreover, a “distance” between the labels can be defined that increases exponentially with time. 