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

Simon, Barry (1983) Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase. Physical Review Letters, 51 (24). pp. 2167-2170. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514087

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.51.2167DOIArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
NSFMCS-81-20833
Issue or Number:24
Classification Code:PACS numbers: 03.65.Db, 02.40.+m
Record Number:CaltechAUTHORS:20180417-104514087
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514087
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85897
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:17 Apr 2018 20:47
Last Modified:03 Oct 2019 19:37

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