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H 1 Mathematical topics around fractional quantization - lecture 2

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

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    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

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 24/05/2019
      Date de captation : 25/04/2019
      Collection : Research school ; Analysis and its Applications ; Mathematical Physics
      Format : MP4
      Durée : 01:31:39
      Domaine : Mathematical Physics ; Analysis and its Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-04-25_Rougerie_Part2.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 Congrès : https://conferences.cirm-math.fr/1982.html

    Citation Data

    DOI : 10.24350/CIRM.V.19527903
    Cite this video as: Rougerie, Nicolas (2019). Mathematical topics around fractional quantization - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19527903
    URI : http://dx.doi.org/10.24350/CIRM.V.19527903


    Voir aussi

    Bibliographie

    1. After the lectures a few references regarding the spectrum of the magnetic Schrödinger operator were suggested to me. Some general texts: -

    2. Victor Ivrii, Microlocal Analysis, Sharp Spectral Asymptotics and Applications - http://weyl.math.toronto.edu/victor_ivrii/research/monsterbook/

    3. 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

    4. A more specialized paper, but perhaps of more direct use: -

    5. 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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