Dissipation and phase slip in confined superfluid He-4

We give a brief summary of some results that are to appear elsewhere. We ha ve studied a vortex-related mechanism for the non-vanishing thermal resista nce well below the bulk: lambda point of liquid He-4 confined in a long cyl inder. Here we outline the main concept of the proposed physical mechanism. It involves the non-equilibrium distribution of vortices in the steady sta te when a small heat current flows along the cylinder axis. We have found t hat the probability of the saddle-point vortex: configuration, which depend s exponentially on the length of the vortex, scaled in units of the superfl uid correlation length, is the dominant factor in the thermal resistance.