Generalized hydrodynamics and the acoustic modes of water: Theory and simulation results

We discuss an application of extended hydrodynamics to a model of water, in a range of wave numbers k, where the effect of single-molecule modes must be taken into account together with the collective phenomena underlying sound propagation and dispersion. The calculation of the density-density, energy-density, energy-energy, and longitudinal and transverse current correlation functions from a molecular dynamics simulation of the transferable intermolecular potential with four points (TIP4P) model of water, allows us to obtain the k dependence of the generalized hydrodynamic coefficients. In particular, we have found that the ratio of generalized heat capacities γ(k)=${\mathit{c}}_{\mathit{p}}$(k)/${\mathit{c}}_{\mathit{v}}$(k)≃1 up to k≃1 Å ${}_{}{}^{\mathrm{-}1}{}_{}{}^{}$ and that the correlation between temperature and density fluctuations is negligible at all times, while there is an important frequency dependence of the transport coefficients. This leads to a remarkable simplification of the expression of the Laplace transform of the correlation functions, although models for the transport coefficients are still necessary at the present state of the theory. The frequency dependence of the transport coefficients is necessary to describe correctly the behavior of the density-density and temperature-temperature autocorrelation functions (ACF’s).