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arXiv:quant-ph/9909085 · Physica D Nonlinear Phenomena

Completely mixing quantum open systems and quantum fractals

Ph. Blanchard, Arkadiusz Jadczyk, Robert Olkiewicz

Published Jan 1, 2001• 5 citations
arXivHTMLPDF
DOI
10.1016/s0167-2789(00)00175-5

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Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the mixing behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting spin components is shown to lead to a chaotic jumps on the quantum spin sphere and to generate specific fractal images of a nonlinear iterated function system. (C) 2001 Published by Elsevier Science B.V.
We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.