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Published December 12, 1983 | Published
Journal Article Open

Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase

Abstract

It is shown that the "geometrical phase factor" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. This not only takes the mystery out of Berry's phase factor and provides calculational simple formulas, but makes a connection between Berry's work and that of Thouless et al. This connection allows the author to use Berry's ideas to interpret the integers of Thouless et al. in terms of eigenvalue degeneracies.

Additional Information

© 1983 American Physical Society. (Received 18 October 1983) It is a pleasure to thank D. Robinson and N. Trudinger for the hospitality of the Australian National University, where this work was done, M. Berry for telling me of his work, and B. Souillard for the remark (via M. Berry) that there must be a connection between Berry's work and that of TKN. This research was partially supported by the National Science Foundation through Grant No. MCS-81-20833.

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Published - PhysRevLett.51.2167.pdf

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August 19, 2023
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October 18, 2023