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]
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“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)).”
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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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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