Third Sound and Thermal Conduction in Thin 4He Films*

In a recent paper 1 (henceforth referred to as AHNS) the static Kosterlitz-Thouless picture of superfluidity in two dimensions 2-4 has been generalized to describe dynamic processes in thin 4He films. A detailed comparison between this dynamic theory and data from torsional .oscillator experiments has shown good agreement: In AHNS, the authors also make certain predictions regarding the propagation of third sound and thermal conduction in thin films. In this paper we discuss the theory of these last two phenomena in somewhat more detail, and make comparisons with available experimental data. In Section 2 we deal with the phenomenon of third sound. In Section 2.1 we review the results of AHNS, who calculate third-sound velocity and damping neglecting mass flow out of the film to the vapor phase and assuming isothermal propagation. We show that, close to the critical temperature, relaxing the above assumptions does not alter the main features of the above model. In Section 2.2 we make comparison with published third-sound data. In Section 3 we deal with the phenomenon of steady-state heat conduction. In Section 3.1 we extend the prediction of AHNS to a particular experimental geometry and calculate thermal resistivity. For the geometry