  The ultrafast conversion of coherent excitons into incoherent excitons, as
well as the subsequent exciton diffusion and thermalization, are central topics
in current scientific research due to their relevance in optoelectronics,
photovoltaics and photocatalysis. Current approaches to the exciton dynamics
rely on {\em model} Hamiltonians that depend on already screened
electron-electron and electron-phonon couplings. In this work, we subject the
state-of-the-art methods to scrutiny using the {\em ab initio} Hamiltonian for
electrons and phonons. We offer a rigorous and intuitive proof demonstrating
that the exciton dynamics governed by model Hamiltonians is affected by an
overscreening of the electron-phonon interaction. The introduction of an
auxiliary exciton species, termed the irreducible exciton, enables us to
formulate a theory free from overscreening and derive the excitonic Bloch
equations. These equations describe the time-evolution of coherent,
irreducible, and incoherent excitons during and after the optical excitation.
They are applicable beyond the linear regime, and predict that the total number
of excitons is preserved when the external fields are switched off.
