Rotating Two-Dimensional Mesoscopic Fermi Gases and Nonrelativistic Conformal Invariance
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Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Physics (MPPHS), MSc
Publicerad
2023
Författare
Bekassy, Viktor
Modellbyggare
Tidskriftstitel
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Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Two-dimensional mesoscopic Fermi gases , nonrelativistic conformal invariance , many-body quantum mechanics