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The geometry of (non-Abelian) Landau levels
| Indexado |
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| DOI | 10.1016/J.GEOMPHYS.2020.103649 | ||||
| Año | 2020 | ||||
| Tipo | artículo de investigación |
Citas Totales
Autores Afiliación Chile
Instituciones Chile
% Participación
Internacional
Autores
Afiliación Extranjera
Instituciones
Extranjeras
Abstract
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.
| Ord. | Autor | Género | Institución - País |
|---|---|---|---|
| 1 | De Nittis, Giuseppe | Hombre |
Pontificia Universidad Católica de Chile - Chile
Facultad de Matemáticas - Chile |
| 2 | Gomi, Kiyonori | Hombre |
Tokyo Inst Technol - Japón
Tokyo Institute of Technology - Japón |
| 3 | Moscolari, Massimo | Hombre |
Aalborg Univ - Dinamarca
Aalborg Universitet - Dinamarca Aalborg University - Dinamarca |
| Fuente |
|---|
| FONDECYT |
| Fondecyt Regular |
| JSPS KAKENHI |
| Japan Society for the Promotion of Science |
| Istituto Nazionale di Alta Matematica "Francesco Severi" |
| Natural Sciences |
| Natur og Univers, Det Frie Forskningsråd |
| Danmarks Frie Forskningsfond |
| GNFM-INdAM |
| National Group of Mathematical Physics |
| National Group of Mathematical Physics (GNFM-INdAM) |
| Danish Council for Independent Research -Natural Sciences |
| Natur og Univers, Det Frie Forskningsråd |
| Fondecyt Regular-1190204 |
| Exploratory Research Center on Life and Living Systems, National Institutes of Natural Sciences |
| Fernanda Florido Calvo |
| Agradecimiento |
|---|
| GD's research is supported by the grant Fondecyt Regular-1190204. KG's research is supported by the JSPS KAKENHI Grant Number 15K04871. MM's research is supported by the Grant 8021-00084B of the Danish Council for Independent Research -Natural Sciences. GD is indebted to Jean Bellissard for suggesting him the idea of a magnetic spectral triple based on the Dirac operator DB described in Footnote 2. GD wishes to thank Fernanda Florido Calvo for checking the consistency of the main results during the writing of her Bachelor's thesis. MM is grateful to Horia Cornean for inspiring discussions. MM gratefully acknowledges the support of the National Group of Mathematical Physics (GNFM-INdAM). The largest part of this document was edited in Santiago del Chile and the first version of the draft was completed during the days when "Chile desperto". It is a fact that the first to wake up were the Chilean students. GD loved and admired them for their courage and their desire to make Chile a better place. |
| GD's research is supported by the grant Fondecyt Regular-1190204. KG's research is supported by the JSPS KAKENHI Grant Number 15K04871. MM's research is supported by the Grant 8021-00084B of the Danish Council for Independent Research — Natural Sciences. GD is indebted to Jean Bellissard for suggesting him the idea of a magnetic spectral triple based on the Dirac operator DB described in Footnote 2. GD wishes to thank Fernanda Florido Calvo for checking the consistency of the main results during the writing of her Bachelor's thesis. MM is grateful to Horia Cornean for inspiring discussions. MM gratefully acknowledges the support of the National Group of Mathematical Physics (GNFM-INdAM). The largest part of this document was edited in Santiago del Chile and the first version of the draft was completed during the days when ”Chile despertó”. It is a fact that the first to wake up were the Chilean students. GD loved and admired them for their courage and their desire to make Chile a better place. |
