Magnetic monopoles in quantum adiabatic dynamics and the immersion property of the control manifold

DOI10.1063/1.2345473zbMath1112.81042OpenAlexW2029169700MaRDI QIDQ3442023

David Viennot

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2345473

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Related Items (2)

Geometry of quantum active subspaces and of effective Hamiltonians ⋮ The need for a flat higher gauge structure to describe a Berry phase associated with some resonance phenomena

Cites Work

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• Quantal phase factors accompanying adiabatic changes
• The relation between the Berry and the Anandan–Aharonov connections for U(𝒩) bundles
• Topological aspects of the non-adiabatic Berry phase
• The Bloch wave operator: generalizations and applications: Part I. The time-independent case
• The Bloch wave operator: generalizations and applications: II. The time-dependent case
• Large geometric phases and non-elementary monopoles
• Quantised singularities in the electromagnetic field,
• Geometry of quantum evolution
• Noncyclic geometric phase and its non-Abelian generalization
• Geometric phase, bundle classification, and group representation

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