Hydrodynamic parameters and correlation functions of the polar phase in superfluid 3He

In the main part of this manuscript we present the correlation function description of the polar phase in superfluid 3He in the bulk in the hydrodynamic regime. This is done using the formalism introduced by Mori and Zwanzig and exploited in the hydrodynamic regime by Forster. The present investigation was triggered by recent NMR experiments on superfluid 3He in aerogels of very high porosity which suggested that the superfluid phase found might be different from the A and B phases present in the bulk. It appears from more microscopic calculations that the polar phase is one of the leading alternative candidates. As one of the results, which can only be obtained in the framework of the projector formalism, we find that the characteristic contributions in the hydrodynamic equations which guarantee the correct transformation behavior under rigid rotations are exclusively due to the non-instantaneous reversible contributions from the memory matrix. This result for the polar phase contrasts with that for other systems with spontaneously broken rotational symmetry in real space – which have the same type of contributions in the phenomenological hydrodynamic equations – such as nematic liquid crystals and the superfluid A phase of 3He. In addition to the truly hydrodynamic regime, we study the influence of the magnetic dipole interaction and of a weak external magnetic field thus including the k=0 dynamics relevant for NMR. For the first time we examine the influence of the presence of the aerogel on the reversible and dissipative macroscopic dynamics in the framework of the projector formalism.