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Explore the mathematical physics of two-dimensional abelian anyons through Hartree and magnetic Thomas-Fermi approximations in this 45-minute conference lecture. Delve into the unique properties of these quasi-particles whose exchange phase differs from standard bosonic and fermionic behavior, examining their representation as fermions coupled to magnetic flux tubes in the magnetic gauge picture. Investigate numerical studies of a Hartree approximate model for the ground state of anyon systems in trapping potentials, which leads to a fermionic variant of the Chern-Simons-Schrödinger system. Discover how semi-classical approximations provide qualitatively accurate results for dense systems, with density functional theory of magnetic Thomas-Fermi type successfully capturing the trends observed in numerical calculations. Learn about the intricate relationship between ground state properties and the fraction of magnetic flux units attached to particles, based on collaborative research with Antoine Levitt and Douglas Lundholm presented at the Workshop on Quantum Many-body Systems and Bose-Einstein Condensation from a Mathematical Physics Perspective.
