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Cited by 9,252Quantum Mechanics and ApplicationsQuantum Mechanics and Non-Hermitian PhysicsQuantum and electron transport phenomena

Quantal phase factors accompanying adiabatic changes

Berry, Michael Victor·1984·Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
DOI 10.1098/rspa.1984.0023
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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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Crossref · 10.1098/rspa.1984.0023

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1 of 1 references verified0 citation errors · 0 not checkable

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  • Earlier studies on graphene established quantized energies of LLs for spinless 2D Dirac fermions are ε_n = v_F sgn(n) sqrt(2e|B n|) (n=0, ±1, ±2...).

    “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]

  • The observed phenomenon dwells upon the existence of the Berry phase, leading to the phenomenon of Zitterbewegung.

    “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]

  • By braiding the probes one imprints the Berry (statistical) phase on the ground state.

    “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]

  • The Aharonov-Bohm effect can be interpreted as a special case of the Berry phase.

    “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]

  • The Berry phase is a physically significant phase that accumulates as an eigenstate evolves under a Hamiltonian whose parameters change adiabatically.

    “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]

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Authors
Berry, M. V.
Affiliations
University of Bristol (GB)
Corresponding author
Berry, Michael Victor
ORCID
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
DOI
10.1098/rspa.1984.0023
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
Licence
royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
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 › Atomic and Molecular Physics, and Optics › 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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