Limited sensitivity to analyticity: a manifestation of quantum chaos

Abstract

Classical Hamiltonian systems generally exhibit an intricate mixture of regular and chaotic motions on all scales of phase space. As a nonintegrability parameter K (the “strength of chaos”) is gradually increased, the analyticity domains of functions describing regular-motion components [e.g., Kolmogorov-Arnol’d-Moser (KAM) tori] usually shrink and vanish at the onset of global chaos (breakup of all KAM tori). It is shown that these phenomena have quantum-dynamical analogs in simple but representative classes of model systems, the kicked rotors and the two-sided kicked rotors. Namely, as K is gradually increased, the analyticity domain ℛQE of the quantum-dynamical eigenstates decreases monotonically, and the width of ℛQE in the global-chaos regime vanishes in the semiclassical limit. These phenomena are presented as particular aspects of a more general scenario: As K is increased, ℛQE gradually becomes less sensitive to an increase in the analyticity domain of the system.