Open problems in liquids dynamics: the role of neutron scattering

We review recent inelastic neutron scattering experiments aimed at investigating still open issues in the microscopic dynamics of liquids. It is shown that the interpretation of experimental results is put on solid ground by the application of modern methods of analysis and lineshape modelling which ensure the fulfillment of fundamental physical properties that the spectra must obey. This last condition becomes crucial to avoid overinterpretations of the genuine information conveyed by scattering data, especially when studying weak signals in the dynamic structure factor. Moreover, we highlight the different roles that neutron data presently play compared to molecular dynamics simulations depending on the nature of the sample, including the case of quantum liquids. In particular, we show how neutron measurements remain an indispensable benchmark in assessing the present capabilities of classical and quantum simulation methods. We also mention the potential of statistical methods, such as Bayesian inference, when applied to neutron data analysis and the opportunity they provide in establishing the spectral features without arbitrary assumptions on the model lineshape