antaris
Registriertes Mitglied
Schade dass die Diskussion auf dem Physikerboard nun abgebrochen wurde.
Ich wollte eigentlich noch folgenden Hinweis auf das Phys. Rev. E 68, 046110 geben, da sich offenbar schon Physiker darum Gedanken gemacht haben.
Ich wollte eigentlich noch folgenden Hinweis auf das Phys. Rev. E 68, 046110 geben, da sich offenbar schon Physiker darum Gedanken gemacht haben.
Classical iterated function systems display several inter-
esting mathematical properties and may be applied in various
problems from different branches of physics. In this work we
have generalized the formalism of IFSs introducing the con-
cept of QIFSs. Quantum iterated function systems may be
defined in the space of pure states on a finite-dimensional
Hilbert space HN , or more generally, in the space of density
operators acting on HN . As their classical analogs, QIFSs
allow a certain degree of stochasticity, in the sense that at
each step of time evolution the choice of one of the pre-
scribed quantum maps is random.
This formalism may be applied to describe several prob-
lems of quantum mechanics, including nonunitary dynamics,
processes of decoherence, and quantum measurements. In
fact, the large class of quantum channels, called random ex-
ternal fields may serve directly as examples of a QIFS. Fur-
thermore, for several classical IFSs one may construct the
corresponding QIFSs and analyze the relations between
them. As shown in the last example, one may focus on the
fractal properties of invariant measures of some classical
IFSs and study their quantum counterpart. Thus, the concept
of QIFS allows one to investigate the semiclassical limit of
random quantum systems.
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