The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
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.
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Citations
Cites
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
Gravitation, gauge theories and differential geometry
Eguchi, T., Gilkey, P. B., & Hanson, A. J. (1980) · Physics Reports · doi:10.1016/0370-1573(80)90130-1 · Cited by 1,833
On the Adiabatic Theorem of Quantum Mechanics
Kato, T. (1950) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.5.435 · Cited by 1,055
Analysis, Manifolds and Physics
(2000) · Elsevier eBooks · doi:10.1016/b978-0-444-50473-9.x5000-3 · Cited by 993
Homotopy and Quantization in Condensed Matter Physics
Avron, J. E., Seiler, R., & Simon, B. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.51 · Cited by 600
Self-citationHermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections
Bott, R., & Chern, S. S. (1965) · Acta Mathematica · doi:10.1007/bf02391818 · Cited by 287
Research works printed but not linked: 4
- M. V. Berry, Proceedings of the Como Conference on Chaos, 1983
- A. Messiah, 1962, Quantum Mechanics
- J. von Neumann, 1929, Phys. Z, 30, 467
- J. Avron, 1978, Ann. Phys. (N.Y.), 110, 85, 10.1016/0003-4916(78)90143-4 · doi:10.1016/0003-4916(78)90143-4
Cited by
Berry phase effects on electronic properties
Xiao, D., Chang, M.-C., & Niu, Q. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1959 · Cited by 5,277
Theory of polarization of crystalline solids
King-Smith, R. D., & Vanderbilt, D. (1993) · Physical Review B · doi:10.1103/physrevb.47.1651 · Cited by 4,472
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655
Observation of unidirectional backscattering-immune topological electromagnetic states
Wang, Z., Chong, Y., Joannopoulos, J. D., & Soljačić, M. (2009) · Nature · doi:10.1038/nature08293 · Cited by 3,123
Metadata
- Authors
- Simon, B.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1983-12-12
- Volume
- 51
- Issue
- 24
- Pages
- 2167-2170
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2081112065
- Cited by
- 1,919
- References
- 6
- FWCI
- 10.69
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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