Theoretical Study of Superfluid ^3He in Aerogel

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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.