K Yu Bliokh 2003 J. Phys. A: Math. Gen. 36 1705 doi:10.1088/0305-4470/36/6/313
Generalized geometric phase of a classical oscillator
K Yu Bliokh
Show affiliationsThe equation of a linear oscillator with adiabatically varying eigenfrequency ω(εt) (ε 
1 is the adiabaticity parameter) is considered. The asymptotic solutions to the equation have been obtained to terms of order ε3. It is shown that imaginary terms of order ε2 form a generalized geometric phase determined by the geometry of the system's contour in the plane (ω, ω'). The real terms of orders ε and ε3, as predicted (Bliokh K Yu 2002 J. Math. Phys. 43 5624), do not form geometric amplitudes but are responsible for local relationships between the solution amplitudes and the parameters, that is, for adiabatic invariants.
- PACS
- MSC
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81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
- Subjects
- Dates
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Issue 6 (14 February 2003)
Received 16 August 2002, in final form 29 November 2002
Published 29 January 2003
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Generalized geometric phase of a classical oscillator
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