A Survey on the Classical Limit of Quantum Dynamical Entropies |
| V. Cappellini
“Mark Kac” Complex Systems Research Centre, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland and Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland |
| Full Text PDF |
| Received: 25 05 2007; |
| We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quantum dynamical entropies and the Kolmogorov-Sinai invariant is found only over timescales that are logarithmic in the quantization parameter. |
| DOI: 10.12693/APhysPolA.112.589 PACS numbers: 05.45.-a, 05.45.Mt, 05.45.Ac, 03.65.Fd |