  We investigate the potential of a quantum Boltzmann equation without momentum
conservation for description of strongly correlated electron systems out of
equilibrium. In a spirit similar to dynamical mean field theory (DMFT), the
momentum conservation of the electron-electron scattering is neglected, which
yields a time-dependent occupation function for the equilibrium spectral
function, even in cases where well-defined quasiparticles do not exist. The
main assumption of this method is that the spectral function remains
sufficiently rigid under the non-equilibrium evolution. We compare the result
of the quantum Boltzmann equation to non-equilibrium DMFT simulations for the
case of photo-carrier relaxation in Mott insulators, where processes on very
different timescales emerge, i.e., impact ionization, intra-Hubbard-band
thermalization, and full thermalization. Since quantum Boltzmann simulations
without momentum conservation are computationally cheaper than non-equilibrium
DMFT, this method allows the simulation of more complicated systems or devices,
and to access much longer times.
