A new approach to the density of states of a liquid gives insight into its collective dynamics

Very recent papers about the self dynamics of Lennard-Jones model fluids clearly demonstrated that the properties of the spectrum Z(w) of the velocity autocorrelation function (VAF) fully justify the identification of Z(w) with the density of states (DoS) of the liquid and that access to this single-particle quantity is of invaluable help for the characterization of the whole dynamics of the system. Based on this identification and on the recent progress in the theory of correlation functions we verified the effectiveness of a method that opens the way to the experimental determination of the DoS of a liquid, otherwise only accessible by simulations of the VAF. We show that by means of multi-Lorentzian fits of the self dynamic structure factor Sself(Q,w) at various Q values, the Q to 0 extrapolation required to determine Z(w) from Sself(Q,w) can be performed smoothly, with the further advantage of by-passing completely the problems related to resolution broadening of either experimental (through incoherent neutron scattering measurements) or simulated self spectra. In the test-case we considered to probe the applicability of the method, and regarding the self dynamics of liquid Au as provided by ab initio simulations, further analysis of Z(w) revealed the presence, along with propagating sound waves, of lower frequency modes in liquid gold that were not observed before by means of dynamic structure factor measurements. Additional inspection of the transverse current-current correlation spectra definitely confirmed the transverse nature of such low-frequency excitations. As an unexpected and remarkable by-product of this work, we also demonstrate that only non-hydrodynamic modes contribute to the DoS of a liquid, thus establishing its purely microscopic origin.