The normal current in a thin film of superfluid 3He-A

A thin film of superfluid 3He-A film containing a polar domain wall has a normal current flowing in it even at zero temperature. This current is calculated from the Gorkov-Nambu equations in a way similar to that of Volovik for bulk 3He-A. An earlier calculation by the authors working to first order in gradients yielded a singular normal current (proportional to a delta function). In the present work it is shown that the singular nature is an artefact of the gradient expansion. An additional length scale in the problem smooths out the delta singularity. It is shown that the current obtained has its origins in a zeroth Landau level. (author)