Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field

Details Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field

2006-10-26

arxiv.org/abs/math-ph/0610076v1

Physics

Mathematical Physics

15 pages, no figures

Scientific paper

10.1088/1751-8113/40/36/013

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.

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