Theory of Surface Effects and A・B Transition in Superfluid ^3He

超流体He-3处于典型的各向异性BCS状态，表面效应对这种状态的影响很大。为了研究这一问题，我们发展了一种准经典格林函数方法，它可以统一地处理从镜面散射到扩散散射的表面散射。将该方法应用于超流体He-3薄膜，讨论了A-B相变、超流体密度和自旋动力学，发现A-B相变温度与薄膜宽度和表面粗糙度有关。我们的结果与以前基于Ginzburg-Landau近似的理论是一致的。表面越粗糙，B相越稳定。这与大阪城市大学课题组的实验结果不一致。我们计算了胶片中的超流体密度。当薄膜很薄时，我们发现与第三个声音实验有很好的一致性。我们发现超流质量流经薄膜的变化反映了表面效应对p波序参数的影响。我们计算了B相的核磁共振频移，结果表明在连续横向核磁共振实验中应该发现有限的正移。综上所述，我们发现超流He-3表现出与体相系统明显不同的性质，反映了表面效应。

Superfluid He-3 is in a typical anisotropic BCS state which is known to be affected very much by the surface effect. To study this problem, we developed a quasi-classical Green's function method that can treat surface scattering, from specular scattering to diffusive scattering, in a unified way. We applied the method to superfluid He-3 film and discussed the A-B transition, the superfluid density, spin dynamics.We found how the A-B phase transition temperature depends on the film width as well as on the surface roughness. Our result is consistent with previous theory based on the Ginzburg-Landau approximation. The B phase is more stable when the surface is more rough. This does not agree with an experimental result by Osaka City University Group.We calculated the superfiuid density in film. We find a good agreement with the third sound experiment when the film is thin. We find superfluid mass flow changes across the film that reflects the surface effects on the p-wave order parameter.We calculated the NMR frequency shift in the B-phase and showed that finite positive shift should be found in the cw transverse NMR experiment.In summary we found that superfluid He-3 shows considerably different properties than the bulk system, reflecting the surface effects.