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##

,

Figures 4.2 and
C.1-C.8.
(Figures from chapters 4 and
5 are not repeated in this appendix.)

Figures 4.2 and
C.1 nicely show how the
quantum web develops with increasing number of kicks.
Obviously, for
centered in a regular region of phase
space,
also tends to concentrate in the meshes of the web,
rather than in the channels, where the
phase space density
gets transported away along the classical separatrices rapidly.

In figure C.2,
and are large enough to avoid the formation of a web-like
structure, and the algorithm has to be stopped after only around
500 kicks, because the norm of the computed state has decayed considerably
already.

In the remaining figures of this subsection,
the initial states are
localized enough -- due to the smaller values of --
to yield localized states even for a very large number of kicks.
An exception to this rule is displayed
in figure C.5, where the
large value of leads to the state flowing apart quickly;
note that for
the HUSIMI distribution has developed a
periodic structure that is quite different from the quantum web of
figures 4.2 and
C.1.

It is important to keep in mind that although a localized initial state,
together with small enough and , leads to *localized*
dynamics this does not rule out the existence of a *global*
stochastic web: clearly, the complete web can be obtained by using an
initial state
with nonzero contributions to
in each of the meshes of the classical web.

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Martin Engel 2004-01-01