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Real-Space Description of Dynamics of Liquids

In strongly disordered matter, such as liquids and glasses, atomic and magnetic excitations are heavily damped and partially localized by disorder. Thus, the conventional descriptions in terms of phonons and magnons are inadequate, and we have to consider spatially correlated atomic and spin dynamics in real-space and time. Experimentally this means that the usual representation of dynamics in terms of the dynamic structure factor, S(Q, E), where Q and E are the momentum and energy exchanges in scattering, is insufficient. We propose a real-space description in terms of the dynamic pair-density function (DyPDF) and the Van Hove function (VHF) as an alternative, and discuss recent results on superfluid 4He by inelastic neutron scattering and water by inelastic X-ray scattering. Today much of the objects of research in condensed-matter physics and materials science are highly complex materials. To characterize the dynamics of such complex materials, the real-space approach is likely to become the mainstream method of research.