### Abstract

Quasi-energy spectral series ( epsilon _{nu}(h(cross)), Psi ( epsilon _{nu})) which, in the limit h(cross) to 0, correspond to stable motions of a classical system along closed phase trajectories are built up in terms of a quasi-classical approximation for the Schrodinger equation with an arbitrary T-periodic h(cross)^{-1} (pseudo)differential Hamilton operator. Using the procedure of splitting the quantum-mechanical phase into dynamic and geometric components, the "geometric" contribution of the Aharonov-Anandan phase gamma _{epsilon ( nu}) to the quasi-energy spectrum is calculated. It is shown that the gamma _{epsilon ( nu}) phase, in the adiabatic approximation, coincides with the Berry phase that corresponds to a cyclic evolution of a stable rest-point of a classical system. Some examples are considered.

Original language | English |
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Article number | 019 |

Pages (from-to) | 5653-5672 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 28 |

Issue number | 19 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*28*(19), 5653-5672. [019]. https://doi.org/10.1088/0305-4470/28/19/019

**The Aharonov-Anandan phase for quasi-energy trajectory-coherent states.** / Trifonov, A. Yu; Yevseyevich, A. A.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 28, no. 19, 019, pp. 5653-5672. https://doi.org/10.1088/0305-4470/28/19/019

}

TY - JOUR

T1 - The Aharonov-Anandan phase for quasi-energy trajectory-coherent states

AU - Trifonov, A. Yu

AU - Yevseyevich, A. A.

PY - 1995

Y1 - 1995

N2 - Quasi-energy spectral series ( epsilon nu(h(cross)), Psi ( epsilon nu)) which, in the limit h(cross) to 0, correspond to stable motions of a classical system along closed phase trajectories are built up in terms of a quasi-classical approximation for the Schrodinger equation with an arbitrary T-periodic h(cross)-1 (pseudo)differential Hamilton operator. Using the procedure of splitting the quantum-mechanical phase into dynamic and geometric components, the "geometric" contribution of the Aharonov-Anandan phase gamma epsilon ( nu) to the quasi-energy spectrum is calculated. It is shown that the gamma epsilon ( nu) phase, in the adiabatic approximation, coincides with the Berry phase that corresponds to a cyclic evolution of a stable rest-point of a classical system. Some examples are considered.

AB - Quasi-energy spectral series ( epsilon nu(h(cross)), Psi ( epsilon nu)) which, in the limit h(cross) to 0, correspond to stable motions of a classical system along closed phase trajectories are built up in terms of a quasi-classical approximation for the Schrodinger equation with an arbitrary T-periodic h(cross)-1 (pseudo)differential Hamilton operator. Using the procedure of splitting the quantum-mechanical phase into dynamic and geometric components, the "geometric" contribution of the Aharonov-Anandan phase gamma epsilon ( nu) to the quasi-energy spectrum is calculated. It is shown that the gamma epsilon ( nu) phase, in the adiabatic approximation, coincides with the Berry phase that corresponds to a cyclic evolution of a stable rest-point of a classical system. Some examples are considered.

UR - http://www.scopus.com/inward/record.url?scp=0011673554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011673554&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/19/019

DO - 10.1088/0305-4470/28/19/019

M3 - Article

AN - SCOPUS:0011673554

VL - 28

SP - 5653

EP - 5672

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 19

M1 - 019

ER -