  We propose a Hamiltonian model that describes the interaction between a
vortex line in superfluid $^{4}$He and the gas of elementary excitations. An
equation of irreversible motion for the density operator of the vortex,
regarded as a macroscopic quantum particle with a finite mass, is derived in
the frame of Generalized Master Equations. This enables us to cast the effect
of the coupling as a drag force with one reactive and one dissipative
component, in agreement with the assumption of the phenomenological theories of
vortex mutual friction in the two fluid model.
