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A mean-field model for almost bosonic anyons

Banff International Research Station for Mathematical Innovation and Discovery

Anyons are particles with quantum statistics different from those of bosons and fermions, the only known types of fundamental particles. They can occur only in low dimensions. There is sound theoretical evidence that certain quasi-particles occuring in quantum Hall physics should behave as anyons, although this remains to be unambiguously observed. 2D anyons are formally equivalent to ordinary bosons coupled to magnetic flux tubes. This leads to a many-body Hamiltonian containing long-range (and rather peculiar) two- and three-body interactions. In this talk I shall discuss a mean-field approximation of said Hamiltonian, appropriate for "almost bosonic" 2D anyons. The model we study is based on a new one-particle energy functional with self-consistent magnetic field, and the associated highly nonlinear partial differential equation. A simplified, Thomas-Fermi-like, local density model, shall be derived in a scaling limit. Joint work with Michele Correggi, Romain Duboscq and Douglas Lundholm.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: Université Grenoble-Alpes and CNRS, LPMMC

2017-11-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63512

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/