Mutual friction in helium II: a microscopic approach

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 HVBK equations. We obtain an expression for the mutual friction coefficient $B$ 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.