Quantum correlations for a simple kicked system with mixed phase space

Abstract

We investigate both the classical and quantum dynamics for a simple kicked system (the standard map) that classically has mixed phase space. For initial conditions in a portion of the chaotic region that is close enough to the regular region, the phenomenon of sticking leads to a power-law decay with time of the classical correlation function of a simple observable. Quantum mechanically, we find the same behavior, but with a smaller exponent. We consider various possible explanations of this phenomenon, and settle on a modification of the Meiss--Ott Markov tree model that takes into account quantum limitations on the flux through a turnstile between regions corresponding to states on the tree. Further work is needed to better understand the quantum behavior.

arXiv comment8 pages, 8 figures

References in corpus (12)

• Long-Time Correlations in the Stochastic Regime
• On universality of algebraic decays in Hamiltonian systems
• Average exit times in volume preserving maps
• Effect of Noise on the Standard Mapping
• Flooding of regular islands by chaotic states
• Survey on the role of accelerator modes for anomalous diffusion: The case of the standard map
• Universal Quantum Localizing Transition of a Partial Barrier in a Chaotic Sea
• Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space
• Fluctuations in the relaxation dynamics of mixed chaotic systems
• Universal Exponent for Transport in Mixed Hamiltonian Dynamics
• Poincaré recurrences and Ulam method for the Chirikov standard map
• Temporal flooding of regular islands by chaotic wave packets