Affiliation: College of Arts and Sciences, Department of Physics and Astronomy
Quantum field theories with a complex action suffer from a sign problem in stochastic nonperturbative treatments, making many systems of great interest – such as polarized or mass-imbalanced fermions and QCD at finite baryon density – extremely challenging to treat numerically. Another such system is that of bosons at finite angular momentum; experimentalists have successfully achieved vortex formation in supercooled bosonic atoms, and have measured quantities of interest such as the moment of inertia. However, the rotation results in a complex action, making the usual numerical treatments of the theory unusable. This thesis treats systems of nonrelativistic bosons with finite angular momentum using two approaches. One approach is to determine the virial coefficients using a semi-classical lattice approximation (SCLA). Through this approach, we are able to compute the thermodynamic equation of state of the bosons for finite trapping frequency, rotation, and inter-particle interaction. The second approach uses the complex Langevin (CL) method – a method which employs an extension of the Langevin equation to complex space and circumvents the sign problem to compute the full quantum behavior of a low energy system of interacting, trapped, and rotating bosons. We examine the density and angular momentum of the system using all three methods, but the CL method in principal allows us to compute properties unique to rotating superfluids, in particular to show the formation of density singularities (so-called vortex lattices) and compute the circulation of the fluid around those vortices. This work advances our understanding of the quantum effects of rotation on ultracold bosonic gases in two different limits.