Asymptotic Behaviours of Adiabatic Invariants

Journal Article · Sun Apr 01 04:00:00 EST 1962 · Progress of Theoretical Physics (Kyoto)

DOI:https://doi.org/10.1143/PTP.27.653· OSTI ID:4811769

Watanabe, Yôiti

The asymptotic expansion of Liouville's distribution in a one- dimensional system is investigated. The expansion leads to the adiabatic theorem with respect to the action integral. The first-order invariance with respect to the - slowness parameter epsilon involved in the external distortion is explained in terms of the canonical mapping between two energy curves in the phase plane but at two different instances, which may be found in the one- dimensional system between those two curves having a common area. The canonical mapping determines the mechanism of the external distortion and yields the second- order invariance of the mean action integral when the action integral is averaged over all possible phases at a fixed initial energy, the distortion being imposed on or released from the system in a sufficiently smooth manner.

• Research Organization: Osaka Univ.
• Sponsoring Organization: USDOE
• NSA Number: NSA-16-026422
• OSTI ID: 4811769
• Journal Information: Progress of Theoretical Physics (Kyoto), Journal Name: Progress of Theoretical Physics (Kyoto) Journal Issue: 4 Vol. 27; ISSN 0033-068X
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ADIABATIC INVARIANCE
DIAGRAMS
DIFFERENTIAL EQUATIONS
DISTRIBUTION
ENERGY
INTEGRALS
INVARIANCE PRINCIPLE
LIOUVILLE EQUATION
MATHEMATICS
MECHANICS
PHYSICS
QUANTUM MECHANICS
STATISTICS
THERMODYNAMICS