Master thesis presentation Viktor Bekassy, MPPHS

Abstract: Experiments on ultracold atoms offer the exciting possibility of probing quantum gases with exceptional accuracy based on techniques just recently developed. Interactions are tunable, and the effective dimensionality of the gas is adjustable, hence making the ability to prepare these cold quantum gases an appealing opportunity to test theoretical predictions. Here, I present the consequences of a joint scale and conformal invariance in rotating mesoscopic two-dimensional Fermi gases at weak interactions; a previously overlooked system since a quantum anomaly was assumed to break scale and conformal invariance. The presented results provide concrete evidence for the conformal tower structure in the energy spectrum of a non-relativistic conformally invariant interacting system. Furthermore, the conformal symmetry predicts the hyperradial distribution function of the many-body wavefunctions in a closed analytical form which we have confirmed using Metropolis importance sampling. Our results could directly be testable with the current experiments on mesoscopic Fermi gases.

Examiner: Johannes Hofmann

Supervisor: Johannes Hofmann

Opponent: Moritz Lange