Theory of Magnetism and Super-fluid Transition of Liquid He-3

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It is widely accepted that the liquid ^3He undergoes a superfluid phase transition forming p-wave Cooper pairs by aid of so-called paramagnon mediated attractive interaction. This mechanism explains well the stability of the ABM state at higher pressures and temperatures. On the other hand, in the normal state, magnetic properties of liquid ^3He is not well described by the paramagnon theory but rather satisfactory by nearly localized model. Moreover, it is recently reported that in the superfluid ^3He in aerogel, the ABM state does not appear when no magnetic field is applied. It implies that the pairing interaction may change due to the impurity scattering.From these aspects, we have studied (1)the susceptibility of normal liquid ^3He taking into account the spin fluctuation, (2)impurity effects on sound propagation in liquid ^3He in aerogel, (3) Formulation of boundary problem for superfluids and superconductors and its application to surface effect on Meissner diamagnetism of proximity-contact normal superconducting systems. In the study of the susceptibility, we have shown that the Fermi surface singularity gives rise to logarithmic temperature dependence of the susceptibility. In the study of sound in liquid ^3He in aerogel, we found that the motion of aerogel due to the collision drag effect plays a dominant role. We expect this study will contribute to the understanding of impurity effect by aerogel on liquid ^3He and also to the pairing mechanism of liquid ^3He in aerogel. The surface problem is very important in the interpretation of sound propagation, in particular anisotropic superfluid such as ^3He, because the sound is excited by transducers at the surface. We have formulated boundary condition for the quasi-classical theory and now trying to extend the theory such that can handle the dynamical problems.