DISSIPATIVE DYNAMICS OF VORTEX LINES IN SUPERFLUID HE-4

We propose a Hamiltonian model that describes the interaction between a vortex line in superfluid He-4 and the gas of elementary excitations . An equation of irreversible motion for the density operator of the v ortex, 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 reactiv e and one dissipative component, in agreement with the assumption of t he phenomenological theories of vortex mutual friction in the two flui d model.