×

Adiabatic approximation and Berry’s phase in the Heisenberg picture. (English) Zbl 0941.81543

Summary: The adiabatic approximation and Berry’s phase are discussed within the framework of the Heisenberg picture.

MSC:

81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
Full Text: DOI

References:

[1] Berry, M. V., Proc. R. Soc. A, 392, 45 (1984) · Zbl 1113.81306
[2] Messiah, A., (Quantum mechanics, Vol. II (1970), North-Holland: North-Holland Amsterdam)
[3] Simon, B., Phys. Rev. Lett., 51, 2167 (1983)
[4] Wilczek, F.; Zee, A., Phys. Rev. Lett., 52, 2111 (1984)
[5] Bereshogin, P. B.; Pronin, P. I., Int. J. Theor. Phys., 32, 219 (1993) · Zbl 0785.53067
[6] Berry, M. V., (Sharpere, A.; Wilczek, F., Geometric phases in physics (1988), World Scientific: World Scientific Singapore)
[7] Tycko, R., Phys. Rev. Lett., 58, 2281 (1987)
[8] Vidal, J.; Wudka, J., Phys. Rev. A, 44, 5383 (1991)
[9] Arnold, V. I., Mathematical methods of classical mechanics (1978), Springer: Springer New York · Zbl 0386.70001
[10] Hannay, J. H., J. Phys. A, 18, 221 (1985)
[11] Maamache, M.; Provost, J.-P.; Vallee, G., J. Phys. A, 23, 5765 (1990) · Zbl 0723.70017
[12] Landau, L.; Lifshitz, E. M., Mechanics (1976), Pergamon: Pergamon Oxford
[13] Anandan, J.; Aharonov, Y., Phys. Rev. D, 38, 1863 (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.