Mathematical topics around fractional quantization - lecture 1 | Vidéo | Carmin.tv

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Mathematical topics around fractional quantization - lecture 1

By Nicolas Rougerie

Appears in collection : Du quantique au classique / From Quantum to Classical

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.

Information about the video

Date of recording 24/04/2019
Date of publication 24/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19527803
Cite this video Rougerie, Nicolas (24/04/2019). Mathematical topics around fractional quantization - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19527803
URL https://dx.doi.org/10.24350/CIRM.V.19527803

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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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