Nonlinear heat transport near the superfluid transition ofHe4

Abstract
We investigate the effect of a finite heat current Q on the superfluid transition of He4. We perform a renormalization-group (RG) calculation of the temperature profile and of the critical thermal conductivity λT(Q) in the nonlinear-response regime. In the experimentally accessible region close to Tλ we predict the divergence λT(Q)∼Qλy with the effective exponent yλ≊0.31. An experiment is proposed to detect this nonlinear effect. We also present the exact RG result x=(2ν)1 for the depression of the transition temperature Tλ-Tλ(Q)∼Qx.