Quantum Dynamical Entropies and Complexity in Dynamical Systems

Details Quantum Dynamical Entropies and Complexity in Dynamical Systems Quantum Dynamical Entropies and Complexity in Dynamical Systems

2004-03-18

arxiv.org/abs/math-ph/0403035v1

Physics

Mathematical Physics

Ph.D. thesis, LaTeX, 138 pages, 12 figures

Scientific paper

We analyze the behaviour of two quantum dynamical entropies in connection with the classical limit. Using strongly chaotic classical dynamical systems as models (Arnold Cat Maps and Sawtooth Maps), we also propose a discretization procedure that resembles quantization; even in this case, studies of quantum dynamical entropy production are carried out and the connection with the continuous limit is explored. In both case (quantization and discretization) the entropy production converge to the Kolmogorov-Sinai invariant on time-scales that are logarithmic in the quantization (discretization) parameter.

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