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H 2 Emergent anyons in quantum Hall physics

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

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bosons and fermions anyons magnetic gauge picture emergence of fractional statistics tracer particles in a Laughlin liquid Laughlin-quasi holes ansatz derivation of the magnetic gauge Hamiltonian average field approximation questions of the audience

Résumé : Anyons are by definition particles with quantum statistics different from those of bosons and fermions. They can occur only in low dimensions, 2D being the most relevant case for this talk. They have hitherto remained hypothetical, but there is good theoretical evidence that certain quasi-particles occuring in quantum Hall physics should behave as anyons.

I shall consider the case of tracer particles immersed in a so-called Laughlin liquid. I will argue that, under certain circumstances, these become anyons. This is made manifest by the emergence of a particular effective Hamiltonian for their motion. The latter is notoriously hard to solve even in simple cases, and well-controled simplifications are highly desirable. I will discuss a possible mean-field approximation, leading to a one-particle energy functional with self-consistent magnetic field.

Keywords : mathematical physics ; many-body quantum mechanics ; anyons ; fractional quantum Hall effect ; quantum statistics ; Laughlin state ; mean-field approximation

Codes MSC :
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
35Q40 - PDEs in connection with quantum mechanics
35Q55 - NLS-like equations (nonlinear Schrödinger)
81S05 - Canonical quantization, commutation relations and statistics
81V70 - Many-body theory; quantum Hall effect
82B10 - Quantum equilibrium statistical mechanics (general)

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 04/05/16
    Date de captation : 19/04/16
    Collection : Research talks ; Partial Differential Equations ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Durée : 00:56:09
    Domaine : PDE ; Mathematical Physics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-04-19_Rougerie.mp4

Informations sur la rencontre

Nom de la rencontre : Spectral theory of novel materials / Théorie spectrales des nouveaux matériaux
Organisateurs de la rencontre : Exner, Pavel ; Kotani, Motoko ; Kuchment, Peter ; Zagrebnov, Valentin A.
Dates : 18/04/16 - 22/04/2016
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1399.html

Citation Data

DOI : 10.24350/CIRM.V.18961603
Cite this video as: Rougerie, Nicolas (2016). Emergent anyons in quantum Hall physics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18961603
URI : http://dx.doi.org/10.24350/CIRM.V.18961603

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