What will be if, given a pure stationary state on a compact hyperbolic surface, we start applying raising operator every ”adiabatic” second? It turns that during adiabatic time comparable to 1 wavefunction will change as a wave traveling with a finite speed (with respect to the adiabatic time), whereas the semiclassical measure of the system will undergo a controllable transformation possessing a simple geometric description. If adiabatic time goes to infinity then, by quantized Furstenberg Theorem, the system will become quantum uniquely ergodic.

Thus, infinite ascension of a closed system leads to quantum chaos.