A novel approach for studying local spin and atomic dynamics in liquids, glasses and crystalline solids with disorder is discussed. In this approach the dynamic structure factor obtained by inelastic neutron or X-ray scattering is Fourier-transformed to real space into the dynamic atomic pair-density function (DPDF). We discuss the nature of the DPDF and show examples of the results obtained by this method. It is demonstrated that the DPDF primarily represents local dynamics, whereas traveling waves contribute only to broadening the peaks. Thus this method complements the conventional analysis of the dynamic structure factor in terms of dispersion relationship of collective dynamics.
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