Heat transport and self-organized criticality in liquid 4 He close to Tλ

We present a renormalization-group calculation based on model F for the thermal conductivity λT(T,Q) in the presence of a homogeneous heat current Q and gravity. For temperatures below Tλ we obtain a large but finite thermal conductivity corresponding to superfluid He with dissipation. Furthermore, we consider the self-organized critical state where the effects of gravity and heat current cancel each other so that the distance from criticality ∆T = T (z) − Tλ(z) is constant in space and a function of Q. We compare our theoretical results with recent experiments. PACS numbers: 67.40.Pm, 64.60.Ht, 66.60.+a, 64.60.Lx