Stochastic Webs

In subsection 4.1.2
unbounded diffusive motion
has been shown to exist for the
*quantum* kicked harmonic oscillator
in the
*classical*
resonance cases (1.23) defined by
as given by equation (1.33).
What is more, the quantum phase portraits
in subsection 4.1.1
clearly demonstrate that the unbounded *quantum motion* takes place
in just the channels of the *classical periodic stochastic webs*
discussed in section 1.2.
In other words, it has been found
numerically
that there exist quantum stochastic
webs covering the whole phase plane and exhibiting the same symmetries
as their classical counterparts described in chapter 1.

In this section 4.2 I review, along the lines of [BR95], an analytical explanation for these observations, using an argument that relies on exploiting the symmetries of the FLOQUET operator and on constructing groups of mutually commuting translation operators in the phase plane that also commute with the FLOQUET operator. A related, though slightly less transparent, line of reasoning may be found in [BRZ91]. The cases and , belonging to -- see equation (1.30) -- but not to , are discussed here, too, as well as the remaining resonances with .