Frequency-dependent shear viscosity, sound velocity, and sound attenuation near the critical point in liquids. I. Theoretical results

We calculate the hydrodynamic shear and sound mode near the liquid-gas phase transition and predict its values for different frequencies and temperatures. The dynamical parameters that enter the theoretical expressions are apart from static quantities the background values of the Onsager coefficients for the order parameter and the transverse momentum current. We find within the field-theoretical renormalization group formalism the asymptotic scaling functions or the real and imaginary parts of the shear and sound mode in the ω-ξ^-1 plane. Our main concern, however, is the calculation of the nonasymptotic expressions describing the crossover from the analytic background to the asymptotic critial behavior.