Ask Ellingsen

Short presentation

My research is centered on mathematical quantum mechanics. My primary focus is quantum statistics - how systems of identical quantum particles behave together - and in particular the exotic statistics of anyons. My research combines topology, geometry, and analysis. I've also become interested in quantum probability.

I am part of the research group Analysis and PDE:s.

My position is funded in part by the Centre for Interdisciplinary Mathematics, and my supervisor is Douglas Lundholm.

Keywords

• analysis
• anyons
• quantum statistics
• mathematical physics
• quantum physics

Biography

• 2022 - present: PhD student at Uppsala University.
• 2021 - 2022: PhD student at Stockholm University.
• 2020 - 2021: Teaching assistant at KTH.
• 2014 - 2020: Student in the engineering physics programme at KTH. Defended my master's thesis on June 30:th 2020.

Research

My PhD project is concerned with the mathematical description of anyons, a type of quasiparticle that arises in certain low dimensional systems (1 and 2 dimensions). Anyons are interesting because they exhibit fractional (or intermediate) quantum statistics. Traditionally, particles can be classified into two groups based on their statistical behaviour: bosons and fermions. In the 70:s and 80:s, it was realised that in low dimensions there is a multitude of new, more exotic possibilities. These are collectively called anyons.

In my project, I want to study both the fundamental mathematical description and classification of anyons, as well as possible applications. Open questions span from computing the ground state energy of an anyon gas, to figuring out how to use anyons to construct topological quantum computers.