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

Original language	English
Pages (from-to)	1191-1206
Number of pages	16
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	5
DOIs	https://doi.org/10.1088/0305-4470/39/5/012
Publication status	Published - 3 Feb 2006

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/39/5/012

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title = "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 Schr{\"o}dinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.",

author = "Litvinets, {F. N.} and Shapovalov, {Aleksandr Vasilievich} and Trifonov, {A. Yu}",

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AU - Litvinets, F. N.

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

PY - 2006/2/3

Y1 - 2006/2/3

N2 - 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 Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

AB - 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 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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JF - Journal of Physics A: Mathematical and General

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

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