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.
|Number of pages||18|
|Journal||Foundations of Physics|
|State||Published - Feb 1997|
Bibliographical noteFunding Information:
We would like to thank M. Feingold, S. Fishman, U. Smilansky, and F. M. Izrailev for useful discussions and comments. We are especially grateful to M. Feingold for providing us with an efficient computer program for the calculation of the Lyapunov spectra of products of random matrices. This work was partially supported by the Israel Ministry of Science and Technology and the Israel Science Foundation administered by the Israel Academy of Sciences and Humanities.