Classical Limit of Quantum Dynamical Entropies

Abstract

Two non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in the quantisation parameter. The model of the quantised hyperbolic automorphisms of the 2-torus is examined in detail.

LaTeX, 41 pages; v2: small changes and corrected typos

References in corpus (3)

• The classical limit of quantum theory
• Quantum Dynamical Entropies in Discrete Classical Chaos
• On the K-property of quantized Arnold cat maps

Cited by in corpus (8)

• Universality of spectra for interacting quantum chaotic systems
• Quantum dynamical entropy and decoherence rate
• Continuous Limit of Discrete Sawtooth Maps and its Algebraic Framework
• Quantum Dynamical Entropies and Complexity in Dynamical Systems
• Quantum dynamical entropies for discrete classical systems: a comparison
• Symmetry Properties of Quantum Dynamical Entropy
• Relaxation Time of Quantized Toral Maps
• A Survey on the Classical Limit of Quantum Dynamical Entropies