[ExI] symmetrical 11-Venn discovered
scerir
scerir at alice.it
Wed Aug 15 07:49:04 UTC 2012
Anders:
> I wonder if these fractals can be seen as the quantum mechanical analog
> to a random walk of a particle?
Actually if one looks at those "quantum carpets" (link below)
http://www.phy.bris.ac.uk/people/berry_mv/the_papers/berry329.pdf
one has the perception of a sort of "walk", more ordered than random.
Asher Peres wrote in his book: "Are you surprised? If so, this is
the result of having been exposed to unfounded quantum superstitions,
according to which quantum theory is afflicted by more "uncertainty"
than classical mechanics. Exactly the opposite is true: quantum
phenomena are more disciplined than classical ones."
As Berry himself pointed out "A quantum wave packet - representing
an electron in an atom, for example - can be constructed from a
superposition of highly excited stationary states so that it is localized
near a point on the electron's classical orbit. If the packet is released,
it starts to propagate around the orbit. This propagation is guaranteed
by the correspondence principle: for highly excited states, quantum
and classical physics must agree. The packet then spreads along the
orbit, and eventually fills it. (It also spreads transversely - that is
away from the orbit - but that is not important in this context.)
Over very long periods of time, however, something extraordinary
happens: the wave packet contracts and after a time, T_r,
returns from the dead and reconstructs its initial form. This is a
quantum revival. As time goes on, the revivals repeat. In a wide class
of circumstances, the reconstructions are almost perfect."
Maybe there is no quantum chaos, in the sense of exponential sensitivity
to initial conditions. But there are several novel quantum phenomena
which may reflect the presence of a sort of chaos (or very strange attractors).
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