  Collective orders and photo-induced phase transitions in quantum matter can
evolve on timescales which are orders of magnitude slower than the femtosecond
processes related to electronic motion in the solid. Quantum Boltzmann
equations can potentially resolve this separation of timescales, but are often
constructed within a perturbative framework. Here we derive a quantum Boltzmann
equation which only assumes a separation of timescales (taken into account
through the gradient approximation for convolutions in time), but is based on a
non-perturbative scattering integral, and makes no assumption on the spectral
function such as the quasiparticle approximation. In particular, a scattering
integral corresponding to non-equilibrium dynamical mean-field theory is
evaluated in terms of an Anderson impurity model in a non-equilibrium steady
state with prescribed distribution functions. This opens the possibility to
investigate dynamical processes in correlated solids with quantum impurity
solvers designed for the study of non-equilibrium steady states.
