Linearized hydrodynamics of 3 He-A1 : correlation functions and hydrodynamic parameters

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Abstract
The complete set of linearized hydrodynamic equations for the superfluid A1-phase of 3He is derived in the framework of the projector formalism by Mori which has been introduced to hydrodynamics by D. Forster. In contrast to purely phenomenological formulations of hydrodynamic equations the projector description allows to make contact with fully microscopic description like the Green's function technique. The hydrodynamic equations of 3He-A1 are characterized, contrary to the A-phase or the B-phase without external magnetic fields, by various couplings of real and spin space, even if the magnetic dipole energy is neglected. Especially a reversible, purely instantaneous coupling between the longitudinal magnetization density and the superfluid velocity exists giving rise to the « magnetic fountain » effect introduced by M. Liu. The correct dispersion relation for the orbit waves in 3He-A1 is presented for the first time and the similarities and differences of this excitation when compared with the corresponding results for the A-phase in high magnetic fields and for the A-phase without external field are discussed. In addition we find that the velocity as well as the damping of fourth sound reflect the reversible coupling of phase deviation and longitudinal magnetization in addition to the static coupling previously introduced by H. Pleiner and R. Graham. A list of Kubo relations for the transport parameters, reversible as well as irreversible ones, is presented and the static correlation functions of g, δϕ and δ li are discussed for k → 0

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