Nonlinear Dynamic Renormalization-Group Analysis above and below the Superfluid Transition inHe4

The usual power-law description of corrections to dynamic scaling is shown to be inapplicable to the superfluid transition in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. A nonlinear dynamic renormalization-group analysis is presented which treats both large departures from scaling and the possible breakdown of scaling. Recent experimental results on second-sound damping are explained. The temperature dependence for $\frac{(T_{\lambda }-T)}{T_{\lambda }}<{10}^{-4\mathrm{}}$ is predicted to deviate only weakly from the dynamic scaling behavior.