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

In the main part of this manuscript we present the correlation function des cription of the polar phase in superfluid He-3 in the bulk in the hydrodyna mic regime. This is done using the formalism introduced by Mori and Zwanzig and exploited in the hydrodynamic regime by Forster. The present investiga tion was triggered by recent NMR experiments on superfluid He-3 in aerogels of very high porosity which suggested that the superfluid phase found migh t 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 a lternative 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 tra nsformation behavior under rigid rotations are exclusively due to the non-i nstantaneous reversible contributions from the memory matrix. This result f or the polar phase contrasts with that for other systems with spontaneously broken rotational symmetry in real space - which have the same type of con tributions in the phenomenological hydrodynamic equations - such as nematic liquid crystals and the superfluid A phase of He-3. In addition to the tru ly hydrodynamic regime, we study the influence of the magnetic dipole inter action and of a weak external magnetic field thus including the k = 0 dynam ics relevant for NMR. For the first time we examine the influence of the pr esence of the aerogel on the reversible and dissipative macroscopic dynamic s in the framework of the projector formalism, (C) 1999 Elsevier Science B. V. All rights reserved.