Nonlinear heat transport near the superfluid transition of 4He.

Abstract

We investigate the effect of a finite heat current Q on the superfluid transition of $^{4}\mathrm{He}$. We perform a renormalization-group (RG) calculation of the temperature profile and of the critical thermal conductivity ${\ensuremath{\lambda}}_{\mathit{T}}$(Q) in the nonlinear-response regime. In the experimentally accessible region close to ${\mathit{T}}_{\ensuremath{\lambda}}$ we predict the divergence ${\ensuremath{\lambda}}_{\mathit{T}}$(Q)\ensuremath{\sim}${\mathit{Q}}_{\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}\mathit{y}}$ with the effective exponent ${\mathit{y}}_{\ensuremath{\lambda}}$\ensuremath{\approxeq}0.31. An experiment is proposed to detect this nonlinear effect. We also present the exact RG result x=(2\ensuremath{\nu}${)}^{\mathrm{\ensuremath{-}}1}$ for the depression of the transition temperature ${\mathit{T}}_{\ensuremath{\lambda}}$-${\mathit{T}}_{\ensuremath{\lambda}}$(Q)\ensuremath{\sim}${\mathit{Q}}^{\mathit{x}}$.