Limited Sensitivity to Analyticity: A Manifestation of Quantum Chaos

Eli Eisenberg*, Itzhack Dana

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)153-170
Number of pages18
JournalFoundations of Physics
Issue number2
StatePublished - Feb 1997
Externally publishedYes


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