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Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

F. N. Litvinets·A. Yu. Trifonov·A. V. Shapovalov
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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 the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and 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 Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

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F. N. Litvinets, A. Yu. Trifonov, A. V. Shapovalov. 2005-10-15. Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential. https://doi.org/10.1088/0305-4470/39/5/012

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