Journal
JOURNAL OF GEOMETRY AND PHYSICS
Volume 152, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.geomphys.2020.103649
Keywords
Landau Hamiltonian; Non-Abelian magnetic field; Real and Quaternionic vector bundles; Dixmier trace
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Funding
- Fondecyt [Regular-1190204]
- JSPS KAKENHI [15K04871]
- Danish Council for Independent Research -Natural Sciences [8021-00084B]
- National Group of Mathematical Physics (GNFM-INdAM)
- Grants-in-Aid for Scientific Research [15K04871] Funding Source: KAKEN
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The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light of (and with the jargon of) the theory of topological insulators. In particular it is shown that the Landau Hamiltonian has a generalized even time-reversal symmetry (TRS). Secondly, a new tool for the computation of the topological numbers associated with each Landau level is introduced by combining the Dixmier trace and the (resolvent of the) harmonic oscillator. Finally, these results are extended to models with non-Abelian magnetic fields. Two models are investigated in details: the Jaynes-Cummings model and the Quaternionic model. (C) 2020 Elsevier B.V. All rights reserved.
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