Collective dynamics of supercooled water close to the liquid-liquid coexistence lines

We report molecular dynamics simulation results for the collective dynamical properties of supercooled bulk water at 180 K at three different densities, corresponding to different phases whose coexistence has recently been discovered in the supercooled regime. In this study, we focus on the behaviour of the longitudinal and transverse current correlation functions and their relative spectra, which we analyze in detail to understand the dynamical processes responsible for the main features observed. Despite the considerable differences in the structure and densities of the three thermodynamic states considered, the obtained current correlation functions show rather similar behaviour in every case. We show that the longitudinal spectra can only be described in terms of three Lorentzian lines, while the accurate reproduction of the transverse spectra requires at least four separate spectral lines. In fact, the behaviour of the peak frequency of the modes necessary to reproduce the spectra as a function of the wavevector indicates in a clear way the nature of the dynamical process. We demonstrate the presence of collective modes associated with the propagation of both longitudinal and transverse sound along with the important contribution of "optical-like" modes, which point out the relevance of localized motions for a right interpretation of the spectral line shape. The wavevector dependence of the relative contributions of the various modes to the total spectral area is also discussed.