A viscoelastic hydrodynamic theory of density fluctuations in liquids

Long-wavelength longitudinal phonons can propagate in liquids, but whether transverse phonons exist in liquids has been long debated. Moreover, according to the classic hydrodynamic theory, it was believed that the transverse modes have no causal relation to the density fluctuations. However, these points of view are challenged by the recent data measured in the generalized hydrodynamic regime from computer simulations and scattering experiments. Hence, in this work, a viscoelastic hydrodynamic approach is proposed to describe the density fluctuations of supercooled liquids in the generalized hydrodynamic regime. Based on the generalization of the Navier-Stokes stress-strain constitutive relation, viscoelastic temporal response and spatial anisotropic effect are integrated into the framework of the hydrodynamic theory using a time-dependent relaxation tensor. As a result, it is found that liquids may exhibit either transverse excitations or transverse kinetic relaxations, depending on specific viscoelastic responses. Moreover, it is demonstrated that anisotropy naturally leads to a hybrid contribution of longitudinal dynamics and transverse dynamics to the density and current correlation functions.