Finite-size Effects on the Thermal Resistivity of 4He Near the Superfluid Transition

We present measurements of the thermal resistivity ρ(t,L) (t ≡ T/Tλ − 1) near the superfluid transition temperature Tλ of 4He at saturated vapor pressure and confined in glass capillary arrays with rectangular capillary crosssections of spacing L = 1 μm, width w = 10μm, and length d # 1 mm. We expect the finite-size effect in this rectangular geometry to provide a good approximation to that in the ideal parallel-plate geometry. The data coincide within our resolution with previous measurements for cylindrical capillaries of 1 μm radius, indicating that the finite-size scaling-functions for these two geometries are indistinguishable. This stands in contrast to the scaling functions for static properties which, near the transition temperature, depend on the dimensionality of the confinement. The results are consistent with recent Monte Carlo and spin-dynamics simulations, and with renormalization-group calculations for capillaries with square cross section and t !0.