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Adiabatic Berry phase and Hannay angle for open paths. (English) Zbl 0928.46060

Author’s abstract: We obtain the adiabatic Berry phase by defining a generalized gauge potential whose line integral gives the phase holonomy for arbitrary evolution of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain the open-path Hannay angle, we establish a connection between the open-path Berry phase Hannay angle by using the parametrized coherent state approach. Using the semiclassical wave-function, we analyze the open-path Berry phase and obtain the open-path Hannay angle. Further, by expressing the adiabatic Berry phase in terms of the commutator of instantaneous projectors with its differential andusing Wigner representation of operators, we obtain the Poisson bracket between the distribution function and its differential. This enables us to talk about the classical limit of the phase holonomy which yields the angle holonomy for the open path. An operational definition of the Hannay angle is provided based on the idea of the classical limit of the quantum mechanical inner product. A probable application of the open-path Berry phase and Hannay angle to the wave-packet revival phenomena is also pointed out.

MSC:

46N50 Applications of functional analysis in quantum physics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81R30 Coherent states
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References:

[1] Simon, B., Phys. Rev. Lett., 51, 2167 (1983)
[2] Berry, M. V., Proc. R. Soc. London A, 392, 457 (1984)
[3] Hannay, J. H., J. Phys. A, 18, 221 (1985)
[4] Aharonov, Y.; Anandan, J., Phys. Rev. Lett., 58, 1593 (1987)
[5] Samuel, J.; Bhandari, R., Phys. Rev. Lett., 60, 2339 (1988)
[6] Mukunda, N.; Simon, R., Ann. Phys., 228, 20 (1993)
[7] Pati, A. K., Phys. Rev. A, 52, 2576 (1995)
[8] Berry, M. V.; Hannay, J. H., J. Phys. A, 21, L325 (1988)
[9] Anandan, J., Phys. Lett. A, 129, 201 (1988)
[10] Jarzynski, C., Phys. Rev. Lett., 74, 1264 (1995)
[11] Gozzi, E.; Thacker, W. D., Phys. Rev. D, 35, 2388 (1987)
[12] Berry, M. V., J. Phys. A, 18, 15 (1985)
[13] Wu, Y. S.; Li, H. Z., Phys. Rev. B, 38, 11 (1988)
[14] Pancharatnam, S., Proc. Indian Acad. Sci. A, 44, 247 (1956)
[15] Pati, A. K., J. Phys. A, 28, 2087 (1995)
[16] Jain, S. R.; Pati, A. K., Phys. Rev. Lett., 80, 650 (1998)
[17] A. K. Pati, Fluctuation, Time-Correlation Function and Geometric Phase; A. K. Pati, Fluctuation, Time-Correlation Function and Geometric Phase
[18] Golin, S.; Knauf, A.; Marmi, S., Comm. Math. Phys., 123, 95 (1989)
[19] Maamache, M.; Provost, J. P.; Valle’e, G. E., J. Phys. A, 23, 5765 (1990)
[20] Keller, J. B., Ann. Phys. (N.Y.), 4, 180 (1958)
[21] Parker, J.; Stroud, C. R., Phys. Rev. Lett., 56, 716 (1986)
[22] Mead, C. A., Rev. Mod. Phys., 64, 51 (1992)
[23] Wagh, A. G., J. Pure Appl. Phys., 33, 566 (1995)
[24] Wigner, E. P., Phys. Rev., 40, 749 (1932)
[25] Berry, M. V., Phil. Trans. R. Soc. London, 287, 237 (1977)
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