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

A. Yu Trifonov, A. A. Yevseyevich

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5 Citations (Scopus)


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 languageEnglish
Article number019
Pages (from-to)5653-5672
Number of pages20
JournalJournal of Physics A: Mathematical and General
Issue number19
Publication statusPublished - 1995

ASJC Scopus subject areas

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

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