Dynamic scaling near the lambda point of liquid helium and at bicritical points

The critical dynamics of liquid helium and of uniaxial antiferromagnets at bicritical points are studied by means of renorrnalized field theory. The problem of dynamic scaling is analyzed in detail. Explicit calculations are perforrned using the E-expansion in d=4-$\epsilon$ dimensions. Results in one-and two-loop order, i.e. first and second order in $\epsilon$, are obtained for dynamic critical exponents, dynamic transient exponents, amplitude ratios and scaling functions at and above the critical points. For liquid helium, the two-loop results suggest but do not establish, the stability of the dynarnic scaling fixed point. The stability is only weak which implies small values of the dynamic transient exponents and a small ratio w* of relaxation rates of the order parameter and the entropy. The scaling function of the density correlation function is deterrnined to O($\epsilon$=4-d) at and above T$_{\lambda}$. A small value of w* implies pronounced peaks of the frequency spectrurn at finite frequencies at and above T$_{\lambda}$. It also suppresses the ternperature dependence of finite-frequency properties over an enlarged critical region as found in light scattering measurements. The quantitative relation between the value of w* > 0 and observable properties of the frequency spectrum is computed.For bicritical dynarnics with reversible mode-coupling, the one-loop results seem to predict a breakdown of dynarnic scaling even in the restricted sense. In two-loop order, however, dynarnic scaling is restored due to the appearance of contributions that are nonanalytic in $\epsilon$. In the case of an n-component relaxational model, total dynarnic scaling is valid to O($\epsilon^{2}$) both at the bicritical (n $\le$ 3) and the tetracritical (4 $\le$ n < 11) points