The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects

Скорочена інформація про документ
dc.contributor.authorDe Nittis, Giuseppe
dc.contributor.authorSandoval, Maximiliano
dc.date.accessioned2025-12-23T13:10:01Z
dc.date.issued2020
dc.description.abstractThis work provides a first step towards the construction of a noncommutative geometry for the quantum Hall effect in the continuum. Taking inspiration from the ideas developed by Bellissard during the 80's, we build a spectral triple for the 𝐶*-algebra of continuous magnetic operators based on a Dirac operator with compact resolvent. The metric aspects of this spectral triple are studied, and an important piece of Bellissard's theory (the so-called first Connes' formula) is proved.
dc.description.sponsorshipGD's research is supported by the grant Fondecyt Regular - 1190204. MS's research is supported by the grant CONICYT-PFCHA Doctorado Nacional 2018--21181868. GD is indebted to Jean Bellissard, who is the real inspirer of this work. GD would like to cordially thank Chris Bourne, Massimo Moscolari, and Hermann Schulz-Baldes for several inspiring discussions. We would like to thank the anonymous referees for providing very useful suggestions, which significantly improved the quality of this work.
dc.identifier.citationThe Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects. Giuseppe De Nittis and Maximiliano Sandoval. SIGMA 16 (2020), 146, 50 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.146
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 81R60; 58B34; 81R15; 81V70
dc.identifier.otherarXiv:2006.06785
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211073
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleThe Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
dc.typeArticle

Файли

Оригінальний контейнер

Зараз показуємо 1 - 1 з 1
Ескіз
Назва:
146-Nittis.pdf
Розмір:
766.62 KB
Формат:
Adobe Portable Document Format
Завантажити

Контейнер ліцензії

Зараз показуємо 1 - 1 з 1
Ескіз
Назва:
license.txt
Розмір:
817 B
Формат:
Item-specific license agreed upon to submission
Опис:
Завантажити

Колекція

Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік