Structure and X-ray diagnostics in non-equilibrium warm dense matter

We present a quantum theory for the dynamic structure factors in non-equilibrium, non-ideal, two-component warm dense matter. This general framework allows the derivation of expressions for the local field corrections in non-equilibrium. Based on a perturbation expansion of the non-equilibrium polarization function in terms of the interaction strength and taking the Wigner function as input quantity, we calculate the dynamic structure for a variety of typical scenarios and demonstrate typical effects. Example situations include laser heated matter or shock produced warm dense matter. We provide a generalized Chihara decomposition of the total dynamic electron structure factor. The formula features the free electrons, the non-equilibrium ion structure, the generalized non-equilibrium screening cloud and an additional term arising due to not invoking the Born-Oppenheimer approximation. This puts the theory of x-ray scattering in non-equilibrium on a sound theoretical basis and makes x-ray scattering a possible diagnostics for non-equilibrium warm dense matter on all time scales, in particular on femtosecond electronic time scales. We give examples for the expected x-ray scattering signals in laser heated systems and in two-temperature systems. We discuss the possibility to resolve temperature relaxation using x-ray scattering and point out possible problems in the current models used for the description of such relaxation processes.