Quantum Dynamical Entropies and Complexity in Dynamical Systems
Abstract
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 KolmogorovSinai invariant on timescales that are logarithmic in the quantization (discretization) parameter.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:mathph/0403035
 Bibcode:
 2004math.ph...3035C
 Keywords:

 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Mathematics  Mathematical Physics;
 Quantum Physics;
 28D20;
 28D99;
 37A99;
 37D99;
 46L99;
 65P20;
 81Q99
 EPrint:
 Ph.D. thesis, LaTeX, 138 pages, 12 figures