Geometric Phase, Hannay's Angle, and an Exact Action Variable

Details Geometric Phase, Hannay's Angle, and an Exact Action Variable Geometric Phase, Hannay's Angle, and an Exact Action Variable

1999-11-08

arxiv.org/abs/quant-ph/9911029v3

Physical Review Letters 85 (2000) 1141-1145

Physics

Quantum Physics

Submitted to Phys. Rev. Lett. (revised version)

Scientific paper

10.1103/PhysRevLett.85.1141

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.

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