149 research outputs found
Particle Tracks, Events and Quantum Theory
The law of track formation in cloud chambers is derived from the Liouville
equation with a simple Lindblad's type generator that describes coupling
between a quantum particle and a classical, continuous, medium of two--state
detectors. Piecewise deterministic random process (PDP) corresponding to the
Liouville equation is derived. The process consists of pairs (classical
event,quantum jump), interspersed with random periods of continuous (in
general, non--linear) Schroedinger's--type evolution. The classical events are
flips of the detectors -- they account for tracks. Quantum jumps are shown, in
the simplest, homogeneous case, to be identical to those in the early
spontaneous localization model of Ghirardi, Rimini and Weber (GRW). The methods
and results of the present paper allow for an elementary derivation and
numerical simulation of particle track formation and provide an additional
perspective on GRW's proposalComment: 22 page
Events and Piecewise Deterministic Dynamics in Event-Enhanced Quantum Theory
We enhance the standard formalism of quantum theory to enable events. The
concepts of experiment and of measurement are defined. Dynamics is given by
Liouville's equation that couples quantum system to a classical one. It implies
a unique Markov process involving quantum jumps, classical events and
describing sample histories of individual systems.Comment: to appear in Phys. Lett. A, 12 pages, Latex article.st
On Quantum Iterated Function Systems
Quantum Iterated Function System on a complex projective space is defined by
a family of linear operators on a complex Hilbert space. The operators define
both the maps and their probabilities by one algebraic formula. Examples with
conformal maps (relativistic boosts) on the Bloch sphere are discussed.Comment: Latex, 12 pages, 3 figures. Added plot of numerical estimate of the
averaged contraction parameter fro quantum octahedron over the whole range of
the fuzziness parameter. Added a theorem and proof of the uniqueness of the
invariant measure. At the very end added subsection on "open problems
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