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

Litvinets, F. N.; Trifonov, A. Yu.; Shapovalov, A. V.

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

Authors

Litvinets, F. N.

Trifonov, A. Yu.

Shapovalov, A. V.

Description

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.
13 pages, no figures