``Well, in our country,'' said Alice, still panting a
little, ``you'd generally get to somewhere else if you ran very
fast for a long time as we've been doing.''
``A slow sort of country!'' said the Queen. ``Now, here, you see, it takes all the running you can do, to keep in the same place.''
Through the Looking Glass
Having discussed some methods for numerically iterating the quantum map of the kicked harmonic oscillator in the previous chapter, the present chapter is dedicated to describing the results of extensive application of these methods in the case of resonance that classically leads to the emergence of stochastic webs -- see chapter 1. The case of nonresonance is dealt with in chapter 5.
In section 4.1 I show that, as a result of the quantum dynamics, web-like structures in quantum phase space develop which are very similar to the classical stochastic webs. As in the classical case, the emergence of such webs turns out to be associated with diffusive energy growth. These numerical findings are given a theoretical explanation in section 4.2.