Theoretical Study of Superfluid ^3He in Aerogel

气凝胶中的超流体^3He作为研究p波对费米超流体中杂质效应的模型系统近年来受到了广泛的关注。在本课题中，我们研究了a相的核磁共振特性和b相的声传播。作为相关问题，我们还研究了p波超导体Sr_2RuO_4的电子拉曼光谱和超流体^3He，1的横向声阻抗。气凝胶中A相的脉冲核磁共振。虽然已知a相是等自旋配对态，但a相的p波序参量仍未确定。最近，Fomin提出了一种非单一配对状态作为a相的候选。我们研究了Fomin状态的核磁共振特性，发现脉冲核磁共振中频率位移的倾倾角依赖与ABM状态的倾倾角依赖有很大的不同，这与大阪城市大学最近的实验结果一致。声音在气凝胶B相中的传播我们已经在法相中表明，碰撞阻力引起气凝胶的同步运动对声音的传播起主导作用。考虑气凝胶的同时运动，采用Keldysh - Green函数形式，计算了超流体B相中声音的频散关系。假设B相为无间隙BW态，得到的吸声量与实验结果吻合较好。

Superfluid ^3He in aerogel has recently attracted much attention as a model system for studying impurity effects in p-wave pairing Fermi superfluid. In this research project, we have studied on the NMR properties of the A-phase and the sound propagation in B-phase. As related problems, we have also studied the electronic Raman spectra of p-wave superconductor Sr_2RuO_4 and transverse acoustic impedance of superfluid ^3He,1.Pulsed NMR in the A phase in aerogel.Although it is known that the A-phase is an equal spin pairing state, the p-wave order parameter in the A-phase is still not identified. Recently Fomin proposed a non-unitary pairing state as a candidate for the A-phase. We have studied the NMR properties of Fomin's state and shown that the tipping angle dependence of the frequency shift in pulsed NMR is quite different from that of the ABM state, which is in agreement with a recent experiment by Osaka City University Group.2.Sound propagation in the B phase in aerogelWe have alredy shown in the normal phase that the simultaneous motion of the aerogel caused by collision drag force plays a dominant role in the propagation of sound. Taking the simultaneous motion of aerogel into account and using the Keldysh Green function formalism, we have calculated the dispersion relation of the sound in the superfluid B phase. Assuming that the B phase is a gapless BW state, we obtained a sound absorption which is in good agreement with experiments.