PDEA Seminar: Nonlinear Landau levels in the almost-bosonic anyon gas

Abstract: I will report on recent joint work with Ataei, Ellingsen, Getzner, Girardot, and Nguyen concerning analytical and numerical analysis for the many-anyon quantum gas confined in a plane and a trapping potential. We consider a limit where the particles are close to bosonic and parametrized by a small magnetic flux attachment and an additional "spin-orbit" interaction parameter. The low-energy landscape of the emerging effective nonlinear and nonlocal Chern-Simons-Schrödinger energy functional can then be explored using a concept of "nonlinear Landau levels", with explicit supersymmetric soliton solutions found by Jackiw and Pi in the early 1990s. Our present work is in a sense a culmination of ca 15 years of mathematical investigations into the fundamental exchange-vs-exclusion problem for intermediate quantum statistics. Reference: arxiv:2510.14679

Participate on site or via Zoom link, meeting ID: 67226102216. Ensure Zoom access by contacting the organisers in advance.

This is a seminar in the PDEs and Applications seminar series.