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，受表面效应影响较大。为了研究这一问题，我们提出了一种准经典格林函数方法，可以统一地处理从镜面散射到扩散散射的表面散射。我们将该方法应用于超流He-3薄膜，讨论了A-B跃迁、超流密度、自旋动力学。我们发现A-B相变温度不仅与表面粗糙度有关，还与薄膜宽度有关。我们的结果与先前基于金兹堡-朗道近似的理论一致。表面越粗糙，B相越稳定。这与大阪城市大学小组的实验结果不一致。我们计算了薄膜中的超流体密度。当薄膜较薄时，与第三次声音实验结果吻合较好。我们发现超流体质量在膜上的流动变化反映了表面效应对p波阶参量的影响。我们计算了b相的核磁共振频移，发现在连续波横向核磁共振实验中存在有限的正频移。综上所述，我们发现He-3超流体表现出与整体体系明显不同的性质，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.