A viscoelastic hydrodynamic theory of acoustic excitations in liquids

Long wavelength longitudinal phonons can propagate in liquids, but whether transverse phonons exist in liquids has been long debated. The classic hydrodynamic theory refutes the existence of transverse phonons in liquids because the transverse current fluctuation is not directly coupled with the density fluctuation and the Brillouin zone is not well-defined. In this work, we generalize the hydrodynamic theory by introducing viscoelastic response and longitudinal-transverse coupling into the stress tensor in the hydrodynamic equations. As a result, the transverse acoustic excitation emerges not only in the current correlation functions but also in the dynamic structure factor, which directly characterizes the density fluctuation. From this derivation, we show the Ioffe-Regel phonon localization condition can be determined. This framework demonstrates another route to generalize the hydrodynamic theory, where the stress tensor plays a similar role as the memory function in the existing generalized hydrodynamics or memory-function approach.