Scaling and universality of the thermal conductivity of liquid 4He near the superfluid transition and in restricted geometries Original Research Article

We present measurements of the thermal conductivity λ(t, P, L) = l/ρ(t, P, L) near the superfluid transition of 4He at saturated vapor pressure and confined in cylindrical geometries with radii L = 0.5 and 1.0 μm (t ≡ T/Tλ(P) − 1). For L = 1.0 μm measurements at six pressures P are presented. At and above Tλ the data are consistent with a universal scaling function F(X) = (L/ξo)x/ν(ρ/ρ0), X = (L/ξo)1/νt valid for all P (ρ0 and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity ρ(t, P, ∞) = ρ0tx and ξ = ξ0t−ν is the correlation length). Indications of breakdown of scaling and universality are observed below Tλ.