Berry phases for 3D Hartree type equations with a quadratic potential   and a uniform magnetic field
  A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time.   A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Hartree type equation. For the solutions constructed, the Berry phases are found in explicit form. 
F.N. Litvinets, A.V. Shapovalov, and A.Yu. Trifonov