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 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrodinger equation is formulated for the Gross–Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.