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

A. Yu Trifonov, A. A. Yevseyevich

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Article number019
Pages (from-to)5653-5672
Number of pages20
JournalJournal of Physics A: Mathematical and General
Volume28
Issue number19
DOIs
Publication statusPublished - 1995

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Coherent States
trajectories
Trajectory
Energy
approximation
energy spectra
Berry Phase
operators
Schrodinger Equation
energy
Approximation
Energy Spectrum
Closed
Series
Motion
Arbitrary
Operator

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Physics A: Mathematical and General, Vol. 28, No. 19, 019, 1995, p. 5653-5672.

Research output: Contribution to journalArticle

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