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

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 $T\gg 1$ 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