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Mathematical topics around fractional quantization - lecture 1
Post-edited
Authors : Rougerie, Nicolas (Author of the conference)
CIRM (Publisher )
81Sxx - General quantum mechanics and problems of quantization
81V70 - Many-body theory; quantum Hall effect
CIRM (Publisher )
Abstract :
The 1983 discovery of the fractional quantum Hall effect marks a milestone in condensed matter physics: systems of “ordinary particles at ordinary energies” displayed highly exotic effects, most notably fractional quantum numbers. It was later recognized that this was due to emergent quasi-particles carrying a fraction of the charge of an electron. It was also conjectured that these quasi-particles had fractional statistics, i.e. a behavior interpolating between that of bosons and fermions, the only two types of fundamental particles.
These lectures will be an introduction to the basic physics of the fractional quantum Hall effect, with an emphasis on the challenges to rigorous many-body quantum mechanics emerging thereof. Some progress has been made on some of these, but lots remains to be done, and open problems will be mentioned.
After the lectures a few references regarding the spectrum of the magnetic Schrödinger operator were suggested to me.
See the bibiography below.
Thanks to Alix Deleporte, Frédéric Faure, Stéphane Nonnenmacher and others for discussions relative to the magnetic Weyl law.
MSC Codes : These lectures will be an introduction to the basic physics of the fractional quantum Hall effect, with an emphasis on the challenges to rigorous many-body quantum mechanics emerging thereof. Some progress has been made on some of these, but lots remains to be done, and open problems will be mentioned.
After the lectures a few references regarding the spectrum of the magnetic Schrödinger operator were suggested to me.
See the bibiography below.
Thanks to Alix Deleporte, Frédéric Faure, Stéphane Nonnenmacher and others for discussions relative to the magnetic Weyl law.
81Sxx - General quantum mechanics and problems of quantization
81V70 - Many-body theory; quantum Hall effect
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 24/05/2019 Conference Date : 24/04/2019 Subseries : Research School arXiv category : Analysis of PDEs ; Mathematical Physics Mathematical Area(s) : Mathematical Physics ; Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 01:37:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-24_Rougerie_Part1.mp4 
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Information on the Event
Event Title : Du quantique au classique / From Quantum to ClassicalEvent Organizers : Nonnenmacher, Stéphane ; Sabin, Julien Dates : 22/04/2019 - 26/04/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/1982.html
Citation Data
DOI : 10.24350/CIRM.V.19527803Cite this video as: Rougerie, Nicolas (2019). Mathematical topics around fractional quantization - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19527803 URI : http://dx.doi.org/10.24350/CIRM.V.19527803 |
See Also
- [Multi angle] Semiclassical behaviour of quantum eigenstates - lecture 2 / Author of the conference Rivière, Gabriel.
- [Multi angle] Mathematical topics around fractional quantization - lecture 2 / Author of the conference Rougerie, Nicolas.
- [Multi angle] Semiclassical behaviour of quantum eigenstates - lecture 1 / Author of the conference Rivière, Gabriel.
Bibliography
- After the lectures a few references regarding the spectrum of the magnetic Schrödinger operator were suggested to me. Some general texts: -
- Victor Ivrii, Microlocal Analysis, Sharp Spectral Asymptotics and Applications - http://weyl.math.toronto.edu/victor_ivrii/research/monsterbook/
- Nicolas Raymond, Bound States of the Magnetic Schrödinger Operator, EMS Tracts in Mathematics Vol. 27 (2017) - https://www.ems-ph.org/books/book.php?proj_nr=212
- A more specialized paper, but perhaps of more direct use:
- - Yves Colin de Verdière, L'asymptotique de Weyl pour les bouteilles magnétiques, Communications in Mathematical Physics 105, 327--335 (1986) - http://dx.doi.org/10.1007/BF01211105
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