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

Lisok, A. L.; Trifonov, A. Yu.; Shapovalov, A. V.

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

Authors

Lisok, A. L.

Trifonov, A. Yu.

Shapovalov, A. V.

Description

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.
17 pages