Progress in the Understanding of Liquids Dynamics via a General Theory of Correlation Functions

This work provides a comprehensive picture of the advances that the exponential expansion theory (EET) of autocorrelation functions relevant to liquids dynamics made possible in the last decade up to very recent times. The role of both longitudinal and transverse collective excitations in liquids is investigated by studying the main autocorrelation functions typically obtained either experimentally (when possible) or through molecular dynamics simulations. Examples for some classes of liquids are provided, especially intended for the understanding of dispersion curves, i.e., the collective mode frequencies as a function of the wavevector Q, which is inversely proportional to the length scale at which microscopic processes are probed. The main result of this work is the ubiquitous observation that the EET method works extremely well for all considered autocorrelation functions or spectra, either experimental or simulated. This paper provides also, in its final part, important hints for future research, based on an integration of the EET lineshape description within Bayesian inference analysis.