Quasi-energy spectral series and the Aharonov-Anandan phase for the nonlocal Gross--Pitaevsky equation

Details Quasi-energy spectral series and the Aharonov-Anandan phase for the nonlocal Gross--Pitaevsky equation Quasi-energy spectral series and the Aharonov-Anandan phase for the nonlocal Gross--Pitaevsky equation

2006-12-05

arxiv.org/abs/math-ph/0612017v2

Physics

Mathematical Physics

17 pages

Scientific paper

For the nonlocal $T$-periodic Gross-Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter $\hbar$, $\hbar\to0$, up to $O(\hbar^{3/2})$ have been constructed. The quasi-energy spectral series found correspond to the closed phase trajectories of the Hamilton-Ehrenfest system which are stable in the linear approximation. The monodromy operator of this equation has been constructed to within $\hat O(\hbar^{3/2})$ in the class of trajectory-concentrated functions. The Aharonov-Anandan phases have been calculated for the quasi-energy states.

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