Density correlation function and dynamic transient exponents for liquid helium at and aboveT λ

The critical dynamics of liquid helium are studied by means of renormalized field theory on the basis of the symmetric planar-spin model of Halperin, Hohenberg, and Siggia. The stability problem of the dynamic fixed point is discussed in detail. Two-loop results suggest, but do not establish, the stability of the dynamic scaling fixed point. The previously found small fixed point valuew ^*~O(0.15) is tentatively confirmed which implies a small ratio of relaxation rates of the order parameter and the entropy. The ensuing dynamic transient exponents are calculated. The density correlation function is determined toO(ε=4?d) at and aboveT _λ. Its properties in the casew ^*?1 provide quantitative support for the recently proposed explanation of the discrepancy between theory and light scattering experiments. A small value ofw ^* implies pronounced peaks of the frequency spectrum at finite frequencies at and aboveT _λ. It also suppresses the temperature dependence of finite-frequency properties over an enlarged critical region as found in light scattering measurements. The quantitative relation between the value ofw ^*>0 and observable properties of the frequency spectrum is computed.