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

F. N. Litvinets·A. V. Shapovalov·A. Yu. Trifonov
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Abstract

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 Schrödinger equation is formulated for the Hartree type equation. For the solutions constructed, the Berry phases are found in explicit form.

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F. N. Litvinets, A. V. Shapovalov, A. Yu. Trifonov. 2006-10-26. Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field. https://doi.org/10.1088/1751-8113/40/36/013

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