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

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

2005-10-15

arxiv.org/abs/math-ph/0510054v1

J. Phys. A: Math. Gen. 39 (2006) 1191--1206

Physics

Mathematical Physics

13 pages, no figures

Scientific paper

10.1088/0305-4470/39/5/012

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 Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

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