### 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 |
---|---|

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 |

### Fingerprint

### ASJC Scopus subject areas

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