Dynamics of superfluid helium-3 in flow channels with restricted geometries

Abstract

The dynamics of superfluid helium-3 in flow channels with transverse sizes smaller than the mean free path of quasiparticles with respect to collisions with each other is considered, taking into account the diffusive reflection of quasiparticles from the walls. For quasiclassical Green functions the boundary conditions obtained by Ovchinnikov for the similar problem in superconductors have been used. Equations are derived defining the behavior of the difference between chemical potentials of normal and superfluid components of helium-3. These equations describe a phenomenon similar to the branch imbalance (or charge imbalance) in superconductors, and determine the relaxation depth of the pressure gradient in superfluid helium-3. The time-dependent Ginzburg-Landau equations are also obtained for the order parameter in the case when the transverse size of the channel is close to the critical value when the superfluid transition temperature goes to zero. The approach makes it possible to study theoretically effects related to the overcritical flows of superfluid helium-3 through narrow channels under pressure.