Critical dynamics of diluteHe3-He4mixtures

The universal scaling functions that describe the crossover of the thermal conductivity and diffusion constant of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ above $T_{\lambda }$, from their behavior in pure helium to that characteristic of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures, along the $\lambda$ line, are calculated to first order in $\epsilon =4-d$ along with the leading correction terms. The crossover exponent is determined to all orders in $\epsilon$ which implies that the thermal conductivity at $T_{\lambda }$ varies inversely with the concentration.