A simple model of superfluid ³He in nematically ordered aerogel

Abstract

Recent experiments have been made with helium-3 immersed in a new type of aerogel. This aerogel consists of aluminium oxide strands, which are directed along roughly the same direction at macroscopic length scale. In this thesis we propose a simple theoretical model of this so called nematically ordered aerogel, and study the model using the Ginzburg-Landau theory of superfluidity. Because of the complexity of the theory, it is necessary to rely on numerical methods. We use two different iterative methods, Newton’s method and Conjugate Gradient method, to numerically minimise the Ginzburg-Landau free energy.

Numerical simulations show that there are three different stable superfluid phases, A-like phase, B-like phase and polar phase. We determine the symmetries of these phases, because the symmetries provide a way to classify different phases. We then present phase diagrams for the model with different boundary conditions and parameters. We also try adding randomness to the model.

A notable result is that the normal-superfluid transition is always from the normal phase to the polar phase. A comparison between the experimental phase diagram and the theoretical phase diagrams shows that the model can explain the experiments qualitatively, but not quantitatively.