Thermal Transport and Dissipation in Two-Dimensional Superfluid HELIUM-4.

We have examined the thermal conductivity of unsaturated helium films on a stainless steel substrate near the super -fluid transition, both as a function of temperature and as a function of heat carried by film. We have analyzed the data in terms of vortex dynamics as calculated by Ambegaokar, Halperin, Nelson and Siggia (AHNS). Near the superfluid transitions we have found that the thermal conductivity increases with decreasing temperature in a manner similar to what would be expected on the basis of the AHNS theory. Below the superfluid transition, our determination of the dependence of thermal conductivity on superfluid velocity differs from the dependence expected on the basis of the AHNS theory. Also, we have examined the specific heat of helium in filled pores of Vycor glass. We have studied in detail the temperature range in which (rho)(,s) is known to vanish with 2/3 power law. No singularity was found in the specific heat. We have analyzed the data in terms of finite size scaling theory and two-scale factor universality.