# Generalized geometric phase of a classical oscillator

@article{Bliokh2003GeneralizedGP, title={Generalized geometric phase of a classical oscillator}, author={Konstantin Y. Bliokh}, journal={Journal of Physics A}, year={2003}, volume={36}, pages={1705-1710} }

The equation of a linear oscillator with adiabatically varying eigenfrequency ω(et) (e 1 is the adiabaticity parameter) is considered. The asymptotic solutions to the equation have been obtained to terms of order e3. It is shown that imaginary terms of order e2 form a generalized geometric phase determined by the geometry of the system's contour in the plane (ω, ω'). The real terms of orders e and e3, as predicted (Bliokh K Yu 2002 J. Math. Phys. 43 5624), do not form geometric amplitudes but…

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