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Phys. Rev. D 35, 2597–2600 (1987)

Some geometrical considerations of Berry’s phase

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J. Anandan
Max-Planck Institut für Physik und Astrophysik, Werner Heisenberg Institut für Physik, Föhringer Ring 6, D-8000 München 40, Federal Republic of Germany; Centre National de la Recherche Scientifique/UA 769, Laboratoire de Physique Théorique, Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France; and Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina 29208

L. Stodolsky
Max-Planck Institut für Physik und Astrophysik, Werner Heisenberg Institut für Physik, Föhringer Ring 6, D-8000 München 40, Federal Republic of Germany

Received 22 May 1986; published in the issue dated 15 April 1987

A group-theoretic treatment is given of the new phase found by Berry in the adiabatic evolution of a quantum-mechanical system in a finite-dimensional Hilbert space. It is shown how the Berry phases for the various eigenstates of the Hamiltonian are obtained from a set of angles associated with a group element. For the special case of a two-level system there is just one such angle which corresponds to the holonomy transformation associated with parallel transport around a closed curve on a sphere.

© 1987 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.35.2597
DOI:
10.1103/PhysRevD.35.2597
PACS:
03.65.Bz, 02.40.+m
 
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