Depression of the superfluid transition inHe4: Renormalization-group theory

We study superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ near ${\mathit{T}}_{\lambda }$ in a homogeneous metastable state where a finite superfluid velocity ${\mathit{v}}_{\mathit{s}}$ is present. Neglecting vortices we perform a renormalization-group calculation of the superfluid current ${\mathit{J}}_{\mathit{s}}$(${\mathit{v}}_{\mathit{s}}$) and determine the critical velocity ${\mathit{v}}_{\mathit{s}\mathit{c}}$(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current ${\mathit{Q}}_{\mathit{c}}$(T) corresponding to ${\mathit{v}}_{\mathit{s}\mathit{c}}$(T) is found which implies a transition temperature ${\mathit{T}}_{\lambda }$(Q)=${\mathit{T}}_{\lambda }$[1-${\mathit{A}}_0$ ${\mathit{Q}}^{\mathit{x}}$] that is lower than ${\mathit{T}}_{\lambda }$. We determine the exact exponent x=[(d-1)ν${]}^{\mathrm{-}1}$≊0.744 in d=3 dimensions and calculate ${\mathit{A}}_0$ in one-loop order. Our results for ${\mathit{A}}_0$ and x are compared with recent experimental data on the depression ${\mathit{T}}_{\lambda }$-${\mathit{T}}_{\lambda }$(Q) of the superfluid transition temperature.