Search for a quantum KAM theorem

The complex mechanisms by which nonlinear classical conservative systems undergo a transition from quasiperiodic to chaotic behavior are now fairly well understood. This transition is associated with a breakdown of quasi-constants of motion (KAM surfaces). There is growing evidence that similar mechanisms may govern the behavior of quantum systems. While K-type mixing behavior has not yet been found, there does appear to be a transition associated with the destruction of a quantum quasi-constant of motion (quantum KAM states) which changes qualitatively the spectrum of quantum systems