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

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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 languageEnglish
Pages (from-to)1191-1206
Number of pages16
JournalJournal of Physics A: Mathematical and General
Volume39
Issue number5
DOIs
Publication statusPublished - 3 Feb 2006

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Berry Phase
Gross-Pitaevskii Equation
Nonlocal Equations
linear equations
Countable
Linear equation
nonlinearity
Nonlinearity
Approximation
approximation
Form
Generalization

ASJC Scopus subject areas

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

Cite this

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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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T1 - Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

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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