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

Abstract

For the nonlocal $T$-periodic Gross-Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter $\hslash$, $\hslash \to 0$, up to $O({\hslash }^{3/2})$ 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 $\hat{O}({\hslash }^{3/2})$ in the class of trajectory-concentrated functions. The Aharonov-Anandan phases have been calculated for the quasi-energy states.

arXiv comment17 pages

References in corpus (1)

• Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential