The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Quantal phase factors accompanying adiabatic changes
Abstract
A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.
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In the citing paper
“Earlier studies on graphene (205,206) established that the quantized energies of LLs for spinless 2D Dirac fermions are ε n = v F sgn(n) 2e |B n| (n = 0, ±1, ±2. . .), 5.”
From Transport of Topological Semimetals (2019) · cites this paper as [205]
In the citing paper
“We theoretically demonstrate that the observed phenomenon dwells upon the existence of the Berry phase [3], leading to the fundamental phenomenon of Zitterbewegung, first introduced by Schrödinger [80] in the context of relativistic electrons.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [3]
In the citing paper
“In other words, by braiding the probes one imprints the Berry (statistical) phase [3] on the ground state.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [3]
In the citing paper
“Efekt se može interpretirati kao specijalni sluˇ caj Berryjeve faze [3].”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [3]
In the citing paper
“The idea of the Berry phase (49) is that, as an eigenstate evolves under a Hamiltonian whose parameters change adiabatically, there is a physically significant phase that accumulates.”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [49]
In the citing paper
“Here, it is important to stress that the high efficiency is not only limited to linear polarization states[26, 28], but also includes circularly polarized light[31, 32].”
From Plasmonic metagratings for simultaneous determination of Stokes parameters (2015) · cites this paper as [32]
Citations
Cites
Concept of nonintegrable phase factors and global formulation of gauge fields
Wu, T. T., & Yang, C. N. (1975) · Physical Review D · doi:10.1103/physrevd.12.3845 · Cited by 1,196 · cited 1×
“The dependence on phase is of the following kind: if | ri)-> exp {ijn(R)} \n)then (n| Wn)-> + iV/£ (in another context the importance of such gauge transformations has been emphasized by Wu & Yang (1975)).”
Background
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Cited by
Sorted by citations
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Gisin, N., Ribordy, G., Tittel, W., & Zbinden, H. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.145 · Cited by 8,515
Flat optics with designer metasurfaces
Yu, N., & Capasso, F. (2014) · Nature Materials · doi:10.1038/nmat3839 · Cited by 5,984
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
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H., & Ong, N. P. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1539 · Cited by 4,798
Metadata
- Authors
- Berry, M. V.
- Affiliations
- University of Bristol (GB)
- Corresponding author
- Berry, Michael Victor
- Venue
- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1984-03-08
- Volume
- 392
- Issue
- 1802
- Pages
- 45-57
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W2097780038
- Cited by
- 9,252
- References
- 1
- Citations by year
- 2026: 353 · 2025: 403 · 2024: 404 · 2023: 465 · 2022: 420 · 2021: 496 · 2020: 518 · 2019: 428 · 2018: 427 · 2017: 396 · 2016: 343 · 2015: 281 · 2014: 265 · 2013: 274 · 2012: 274
- FWCI
- 18.94
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Quantum and electron transport phenomena
- Keywords
- Berry phase, adiabatic phase, dynamical phase, degeneracy, real symmetric matrices, spin precession, Aharonov-Bohm effect, topological phases
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