Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

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Abstract

A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. 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 Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form.

Original languageEnglish
Article number013
Pages (from-to)11129-11149
Number of pages21
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number36
DOIs
Publication statusPublished - 7 Sep 2007

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Berry Phase
Linear equations
Magnetic Field
Magnetic fields
linear equations
magnetic fields
Countable
Linear equation
Approximation
approximation
Form
Generalization

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

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title = "Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field",
abstract = "A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. 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 Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form.",
author = "Litvinets, {F. N.} and Shapovalov, {Aleksandr Vasilievich} and Trifonov, {A. Yu}",
year = "2007",
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AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

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AB - A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. 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 Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form.

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