Chaotic Rotation from Nonlinear Quantum Mechanics. II

The approach proposed in the first part of this paper is illustrated by two examples. The first one involves the H\'enon-Heiles model. A small wave packet, initially localized in the classically chaotic region, evolves so that $〈x〉$ and $〈{x}^{2}〉$ rapidly reach their equilibrium values. The second example makes use of a pair of rotators with nonlinear coupling. The matrix elements of ${J}_{z}$ , in the energy representation, are pseudorandom in the energy range which is classically chaotic, but obey selection rules in the classically regular energy range.The approach proposed in the first part of this paper is illustrated by two examples. The first one involves the H\'enon-Heiles model. A small wave packet, initially localized in the classically chaotic region, evolves so that $〈x〉$ and $〈{x}^{2}〉$ rapidly reach their equilibrium values. The second example makes use of a pair of rotators with nonlinear coupling. The matrix elements of ${J}_{z}$, in the energy representation, are pseudorandom in the energy range which is classically chaotic, but obey selection rules in the classically regular energy range.

Physical Review AJul 1, 1984114 citations

Quantum mechanics and quantum chaos

Robert C. Bishop

Institute of Physics eBooksMay 1, 20250 citations

Complex Classical Mechanics and Quantum Chaos(Bifurcation Phenomena in Nonlinear Systems and Theory of Dynamical Systems)

Satoshi Adachi

Abstruct.The semiclassical coherent state path integral developed by Klauder is evaluated numerically for a chaotic system (the kicked rotator).This evaluation needs the complexfied classical dynamics of the system and involves a proper treatment of the Stokes phenomenon caused by a new caustic, named \ l a n g l e \ l a n g l e Phase Space Caustic (PSC) ) \ r a n g l e .It is revealed that the chaotic natute of the dynamics produces PSC's.This investigation suggests that complex classical mechanics has a clear physical reality.Abstruct.The semiclassical coherent state path integral developed by Klauder is evaluated numerically for a chaotic system (the kicked rotator).This evaluation needs the complexfied classical dynamics of the system and involves a proper treatment of the Stokes phenomenon caused by a new caustic, named \ l a n g l e \ l a n g l e Phase Space Caustic (PSC) ) \ r a n g l e .It is revealed that the chaotic natute of the dynamics produces PSC's.This investigation suggests that complex classical mechanics has a clear physical reality.

数理解析研究所講究録Dec 1, 19890 citations

〈x〉

and

〈{x}^{2}〉

rapidly reach their equilibrium values. The second example makes use of a pair of rotators with nonlinear coupling. The matrix elements of

{J}_{z}

, in the energy representation, are pseudorandom in the energy range which is classically chaotic, but obey selection rules in the classically regular energy range.