CIRM - Videos & books Library - Mathematical topics around fractional quantization

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Auteurs : Rougerie, Nicolas (Auteur de la conférence)
CIRM (Editeur )

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special values of the filling factor interacting Landau hamiltonian energy scales in the quantum Hall effect ground state wave function integer quantum Hall effect spectrum of the magnetic laplacian Weyl law for the magnetic laplacian gap above the integer quantum Hall effect ground state fractional quantum Hall effect Laughlin's state density of the Laughlin state

Résumé : 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.

Codes MSC :
81Sxx - General quantum mechanics and problems of quantization
81V70 - Many-body theory; quantum Hall effect

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2019-04-24_Rougerie_Part1.mp4

Informations sur la Rencontre

Nom de la Rencontre : Du quantique au classique / From Quantum to Classical
Organisateurs de la Rencontre : Nonnenmacher, Stéphane ; Sabin, Julien
Dates : 22/04/2019 - 26/04/2019
Année de la rencontre : 2019
URL de la Rencontre : https://conferences.cirm-math.fr/1982.html

Données de citation

DOI : 10.24350/CIRM.V.19527803
Citer cette vidéo: 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

Voir Aussi

[Multi angle] Semiclassical behaviour of quantum eigenstates - lecture 2 / Auteur de la conférence Rivière, Gabriel.
[Multi angle] Mathematical topics around fractional quantization - lecture 2 / Auteur de la conférence Rougerie, Nicolas.
[Multi angle] Semiclassical behaviour of quantum eigenstates - lecture 1 / Auteur de la conférence Rivière, Gabriel.

Bibliographie

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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