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

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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
Issue number36
Publication statusPublished - 7 Sep 2007


ASJC Scopus subject areas

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

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