Mutual friction in helium II: a microscopic approach

Abstract

We develop a microscopic model of mutual friction represented by the dissipative dynamics of a normal fluid flow which interacts with the helical normal modes of vortices comprising a lattice in thermal equilibrium. Such vortices are assumed to interact with the quasiparticles forming the normal fluid through a pseudomomentum-conserving scattering Hamiltonian. We study the approach to equilibrium of the normal fluid flow for temperatures below 1 K, deriving an equation of motion for the quasiparticle pseudomomentum which leads to the expected form predicted by the Hall–Vinen–Bekharevich–Khalatnikov equations. We obtain an expression for the mutual friction coefficient in terms of microscopic parameters, which turns out to be practically independent of the vortex mass for values arising from diverse theories. By comparing our expression of B with previous theoretical estimates, we deduce interesting qualitative features about the excitation of Kelvin modes by the quasiparticle scattering.