  The use of ultra-short laser pulses to pump and probe materials activates a
wealth of processes which involve the coherent and non coherent dynamics of
interacting electrons out of equilibrium. Non equilibrium (NEQ) many body
perturbation theory (MBPT) offers an equation of motion for the density-matrix
of the system which well describes both coherent and non coherent processes. In
the non correlated case there is a clear relation between these two regimes and
the matrix elements of the density-matrix. The same is not true for the
correlated case, where the potential binding of electrons and holes in
excitonic states need to be considered. In the present work we discuss how
NEQ-MBPT can be used to describe the dynamics of both coherent and non-coherent
excitons in the low density regime. The approach presented is well suited for
an ab initio implementation.
