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

We present a renormalization-group calculation based on model F for the thermal conductivity lambda_T(T,Q) in the presence of a homogeneous heat current Q and gravity. For temperatures below T_lambda we obtain a large but finite thermal conductivity corresponding to superfluid 4He 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 delta T = T(z) - T_lambda(z) is constant in space and a function of Q. We compare our theoretical results with recent experiments.