Appearance of Gauge Structure in Simple Dynamical Systems
Abstract
Generalizing a construction of Berry and Simon, we show that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.
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Cyclic transport can lead to non-Abelian geometric phases when the system is prepared in a degenerate state.
“Cyclic transport as discussed above can lead to non-Abelian geometric phases when the system is prepared in a degenerate state [7,6].”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [7]
If a system is prepared in a g_n-fold degenerate state and the degeneracy holds for all R, a cyclic adiabatic evolution can rotate the initial state within the degenerate subspace.
“Ako je sustav pripremljen u g n -degeneriranom stanju i degeneracija vrijedi za sve R , cikliˇ cka adijabatska evolucija može rotirati poˇ cetno stanje unutar degeneriranog potprostora: | ψ n ( T ) 〉 = U dyn U n C | ψ n (0) 〉 .”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [7]
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- Authors
- Wilczek, F., & Zee, A.
- Affiliations
- University of California, Santa Barbara (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1984-06-11
- Volume
- 52
- Issue
- 24
- Pages
- 2111-2114
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2008791564
- Cited by
- 1,775
- References
- 0
- Citations by year
- 2026: 75 · 2025: 70 · 2024: 60 · 2023: 63 · 2022: 84 · 2021: 88 · 2020: 112 · 2019: 69 · 2018: 70 · 2017: 57 · 2016: 60 · 2015: 46 · 2014: 44 · 2013: 53 · 2012: 68
- FWCI
- 9.21
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- Yang-Mills fields, adiabatic evolution, quantum systems, energy level splitting, classical analog, Berry phase
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