Rotating Two-Dimensional Mesoscopic Fermi Gases and Nonrelativistic Conformal Invariance

Abstract

Experiments on ultracold atoms offer the exciting possibility of probing quantum gases with exceptional accuracy based on recently developed techniques. 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. This thesis presents the consequences of a joint scale and conformal invariance in rotating mesoscopic two-dimensional Fermi gases at weak interactions; a previously overlooked system since quantum anomaly was assumed to break scale and conformal invariance. With degenerate perturbation theory, the energy spectrum for mesoscopic particle ensemble is computed, thus providing concrete evidence for the conformal tower structure of a nonrelativistic conformally invariant interacting system. Furthermore, the conformal symmetry predicts the hyperradial distribution function of the many-body wave functions in a closed analytical form, which has been confirmed using Metropolis Monte Carlo sampling. We argue that our results could directly be testable with current experiments on mesoscopic Fermi gases.