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

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/T_λ(P) − 1). For L = 1.0 μm measurements at six pressures P are presented. At and above T_λ the data are consistent with a universal scaling function F(X) = (L/ξ_o)^x/ν(ρ/ρ₀), X = (L/ξ_o)^1/νt valid for all P (ρ₀ and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity ρ(t, P, ∞) = ρ₀t^x and ξ = ξ₀t^−ν is the correlation length). Indications of breakdown of scaling and universality are observed below T_λ.