Crystallographic refinement of collective excitations using standing wave inelastic x-ray scattering

We propose a method for realizing true, real-space imaging of charge dynamics in a periodic system, with angstrom spatial resolution and attosecond time resolution. In this method, inelastic x-ray scattering (IXS) is carried out with a coherent, standing wave source, which provides the off-diagonal elements of the generalized dynamic structure factor, S(q_1,q_2,\omega), allowing complete reconstruction of the inhomogeneous response function of the system, \chi(x_1,x_2,t). The quantity \chi has the physical meaning of a propagator for charge, so allows one to observe - in real time - the disturbance in the electron density created by a point source placed at a specified location, x_1 (on an atom vs. between atoms, for example). This method may be thought of as a generalization of x-ray crystallography that allows refinement of the excited states of a periodic system, rather than just its ground state.