Mutual friction and vortex motion near the superfluid transition

Abstract

The mutual friction parametersB and B′ for a moving vortex are calculated near the superfluid transition. They are proportional to the kinetic coefficient associated with the order parameter and, asT →λ, diverge as (Tλ − T)−1/3, in agreement with experiment. The nonlinear couplings between the order parameter Ψ and the entropym, both the reversible one and the one in the free energy, are found to be crucial in the mutual friction near the λ point. These couplings were neglected in a previous paper by the author. First, the reversible coupling in the dynamic equations makes the chemical potential deviation long-ranged and causes the dissipation to take place only near the vortex core. Second,B′ can diverge asT → Tλ only in the presence of the coupling of the formm|Ψ|2 in the free energy. Thus theE model of Halperin et al., where the latter coupling is absent, cannot explain the critical anomaly ofB′. The helical mode of a single vertex line is also investigated and its dispersion relation is found to be quite different from that at low temperatures. This mode has the same time scale as that of the second-sound mode when the wave vectors are of the order of the inverse correlation length, thus obeying the usual dynamic scaling law. The time correlation functions of the displacement fluctuations of a vortex line are also obtained. The force acting on a moving vortex is calculated and is found to be equal to the classical Magnus force.