Quantum Mechanics of a Particle Confined to a Twisted Ring
Abstract
We derive an effective Hamiltonian for a particle confined to a thin tube which is gently twisted and curved to form a closed loop. The Hamiltonian describes the effect of both the curvature and the torsion of the loop correctly to the second order. Applied to the case of a tube of circular cross section, it reveals complete analogy with the Aharonov-Bohm effect. We also discuss eigenmodes for Möbius-like rings formed by a tube of non-circular cross section.
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The Berry phase is analogous to the Aharonov-Bohm (or Dirac) phase in quantum mechanics.
“At the same time, it shows that the Berry phase is analogous to the Aharonov -Bohm (or Dirac) phase in quantum mechanics [94 -96].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [95]
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Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Bliokh, K. Y. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094009 · Cited by 217 · see citing works
- Authors
- Takagi, S., & Tanzawa, T.
- Affiliations
- Tohoku University (JP)
- Venue
- Progress of Theoretical Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 1992-03
- Volume
- 87
- Issue
- 3
- Pages
- 561-568
- ISSN
- 0033-068X (ISSN-L)
- OpenAlex
- W1995469826
- Cited by
- 57
- References
- 0
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 1 · 2022: 2 · 2021: 2 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 1 · 2015: 1 · 2013: 2 · 2012: 3
- FWCI
- 2.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Progress of Theoretical Physics (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- 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
- Keywords
- effective Hamiltonian, curvature, torsion, Aharonov-Bohm effect, Möbius ring, non-circular cross-section, eigenmodes, thin tubes
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