Quantum control, diffusion

It might be worthwhile to look into H=H₀+μ·E. The driving term cause the diffusion perpendicular to energy surface, and H₀ has diffusion by itself on the energy surface. If D_∥»D_⊥, it can be argued that the quasienergy (Floquet energy) eigenfunctions will be localized exponentially (see D.L. Shepelyansky, Physica D, 28, 103-114 (1987)). Also read Wigner distribution, Arnol'd diffusion.

Flashback: in the XCN isomerization studies (also between-tile hopping in the current study), everything might be broiled down to the comparison between diffusion rates along different directions (in the phase space). If D_∥»D_⊥, then the particle has a good chance to "isomerize" than to "dissociate".

For d>2 degrees of freedom systems, the invariant tori in phase space, being d-dimensional, can not slice the 2d-1 dimensional space of the surface of constant energy. This means for (d>2)-DOF systems the phase space is essentially "ergodic" (Arnol'd diffusion).