Mapping of the unoccupied states and relevant bosonic modes via the time   dependent momentum distribution
  The unoccupied states of complex materials are difficult to measure, yet play a key role in determining their properties. We propose a technique that can measure the unoccupied states, called time-resolved Compton scattering, which measures the time-dependent momentum distribution (TDMD). Using a non-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to a lattice in a pump-probe setup. We find a direct relation between temporal oscillations in the TDMD and the dispersion of the underlying unoccupied states, suggesting that both can be measured by time-resolved Compton scattering. We demonstrate the experimental feasibility by applying the method to a model of MgB$_2$ with realistic material parameters. 
A. F. Kemper, M. Sentef, B. Moritz, C. C. Kao, Z. X. Shen, J. K.   Freericks and T. P. Devereaux
cond-mat.stat-mech cond-mat.mtrl-sci quant-ph