Quantum dynamical entropies for discrete classical systems: a comparison
arXiv:quant-ph/0506254 · doi:10.1088/0305-4470/38/31/003
Abstract
On a family of classical dynamical systems on the 2-torus, we perform a discretization procedure similar to the Anti-Wick quantization. Such a discretization is performed by using a particular class of states, fulfilling an appropriate dynamical localization property, typical of quantum Coherent States. The same set of states is involved in the construction of a quantum entropy, that we test on the discrete approximants; a correspondence with the classical metric entropy of Kolmogorov-Sinai is found only over time scales that are logarithmic in the discretization parameter.
LaTeX, 36 pages. References updated