Simulations of topological defects and impurities in superfluid 3He

The less common helium isotope, 3He, becomes superfluid when the temperature falls below 1 mK. Superfluidity is one indication of a condensation into the same quantum mechanical state. For 3He the condensation into a single state occurs by forming Cooper pairs. In the superfluid state 3He is an ideal substance to study a non-conventional p-wave spin-triplet pairing. This dissertation considers theoretically different topological defects that appear in the superfluid state and the effect of impurities. Vortices and solitons are the most common topological defects that appear in superfluid 3He. They may be observed in both A and B phases by using nuclear magnetic resonance (NMR). Here we consider the A phase vortex texture in the presence of a stable A-B phase boundary. As a result two new possible vortex textures were obtained to exist at the A-B boundary. Both of these surface sheet textures differ from the vortex sheet that appears in the bulk A phase. Different dissipation mechanisms are analyzed by calculating the NMR absorption spectrum caused by solitons. The normal-superfluid relaxation causes only line broadening, but the spin diffusion, which results from the inhomogeneous texture, also shifts the soliton peak to higher frequencies. Typically helium is an ultra-pure liquid without any impurities. Experimentally the effect of impurities on the superfluid state can be investigated by using a very porous aerogel. When the empty space inside aerogel is filled with liquid helium, the aerogel strands act as an impurity and scatter the helium quasiparticles. In this thesis the effect of impurities on superfluid 3He is analyzed by using the quasiclassical theory and by considering two simple scattering models. In the homogeneous scattering model the impurities are assumed to be evenly distributed, the assumption that is often used for superconductors. In the inhomogeneous model the impurity density is allowed to depend on location. Using these models the critical temperature, pair amplitude, and superfluid density for 3He are determined numerically.reviewe