The Geometric Phases and Quasienergy Spectral Series of a Hartree-Type Equation with a Quadratic Potential

Based on the ideology of the complex WKB–Maslov method, the general construction of quasiclassically concentrated solutions is given for Hartree-type equations with a quadratic potential and periodic coefficients. Exact expressions are constructed for the quasienergies and associated quasienergy states. In the construction of solutions, an important role is played by the Hamilton–Ehrenfest system of equations obtained in this work. Explicit expressions are found for the geometric phase of Aharonov–Anandan quasienergy states.     

Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton-Ehrenfest system

We consider the classical equations of motion in quantum means, i.e., the Hamilton-Ehrenfest system. In the semiclassical approximation in the framework of the covariant approach based on these equations, we construct the spectral series of a nonlinear Hartree-type operator corresponding to a rest point. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 26–40, January, 2007.     

Semiclassical spectral series of the two-component Hartree-type operator

In the context of the Maslov complex germ theory, semiclassical spectral series of the two-component nonlinear operator responding for the rest point of the phase curve are constructed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–81, May, 2007.