### 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 language | English |
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Article number | 013 |

Pages (from-to) | 11129-11149 |

Number of pages | 21 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 36 |

DOIs | |

Publication status | Published - 7 Sep 2007 |

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### ASJC Scopus subject areas

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

### Cite this

**Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field.** / Litvinets, F. N.; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 40, no. 36, 013, pp. 11129-11149. https://doi.org/10.1088/1751-8113/40/36/013

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TY - JOUR

T1 - Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

AU - Litvinets, F. N.

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

PY - 2007/9/7

Y1 - 2007/9/7

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=34548258161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548258161&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/40/36/013

DO - 10.1088/1751-8113/40/36/013

M3 - Article

VL - 40

SP - 11129

EP - 11149

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 36

M1 - 013

ER -