Superfluidity in Two Dimensions

This dissertation consists of a study of the following two problems related to the superfluidity in the boson systems in two dimensions. The first problem is the supersymmetric quantum XY model. It is a modification of the quantum rotor model, whose ground state is exactly known. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The three-site terms in the Hamiltonian are perturbatively unimportant, but they are relevant, i.e., they change the universality class of the phase transition from that of a (d + 1) - to a d- dimensional classical XY model. We have studied variational wavefunctions for single particle and collective excitations for this model using Monte Carlo simulation. The second problem is related to the momentum transfer between a superfluid ^4He film and ^4He vapor when the system is not in equilibrium. We obtain an expression for the momentum transfer using Fermi's golden rule assuming that only phonon-like excitations are possible in the film at low temperatures. We compare this expression with a hydrodynamic expression for momentum transfer obtained by solving the diffusion equation for flow velocity of the vapor with slip boundary conditions. From the comparison of the two expressions, we determine the slip at the gas-film interface as a function of temperature and coverage. The results are used to calculate the period shift and dissipation due to viscous drag for a torsional oscillator, and applied to an actual experiment.