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 |
|---|---|
| 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
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 journal › Article
}
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.
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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
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 -