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

Abstract

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/ ρ 0), X = ( L/ ξ o ) 1/ ν t valid for all P ( ρ 0 and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity ρ( t, P, ∞) = ρ 0 t x and ξ = ξ 0 t − ν is the correlation length). Indications of breakdown of scaling and universality are observed below T λ .