# PDEA Seminar: A mathematical introduction to quantum statistics transmutation via magnetic flux attachment

- Date: 17 September 2024, 10:15–11:00
- Location: Ångström Laboratory, 64119
- Type: Seminar
- Lecturer: Douglas Lundholm
- Organiser: Matematiska institutionen
- Contact person: Kaj Nyström

Douglas Lundholm gives a seminar with the title "A mathematical introduction to quantum statistics transmutation via magnetic flux attachment". Welcome!

**Abstract:** Quantum statistics refers to the ways that identical quantum particles may distribute themselves into different energy configurations or probability distributions: Bose-Einstein statistics obeyed by bosons, respectively Fermi-Dirac statistics obeyed by fermions, with the latter being subject to Pauli's exclusion principle. In joint work with Gaultier Lambert and Nicolas Rougerie we have considered a situation in two dimensions and a strong transverse magnetic field in which statistics transmutation can be rigorously proved: by capturing magnetic flux, fermions turn into bosons and vice versa. Our method uses estimates for the characteristic polynomial of the Ginibre ensemble of random matrices. The result also sheds some light on the emergence of intermediate ("fractional") statistics in the fractional quantum Hall effect, and exotic quasi-particles called "anyons", which despite recent breakthrough experimental advances still have a number of technical ambiguities attached to them.

Participate on site or via Zoom link, meeting ID: 67226102216

This is a seminar in the PDEs and Applications seminar series