  The dephasing and relaxation kinetics of bosonic excitons interacting with a
thermal bath of acoustic phonons is studied after coherent pulse excitation.
The kinetics of the induced excitonic polarization is calculated within
Markovian equations both for subcritical and supercritical excitation with
respect to a Bose-Einstein condensation (BEC). For excited densities n below
the critical density n_c, an exponential polarization decay is obtained, which
is characterized by a dephasing rate G=1/T_2. This dephasing rate due to phonon
scattering shows a pronounced exciton-density dependence in the vicinity of the
phase transition. It is well described by the power law G (n-n_c)^2 that can be
understood by linearization of the equations around the equilibrium solution.
Above the critical density we get a non-exponential relaxation to the final
condensate value p^0 with |p(t)|-|p^0| ~1/t that holds for all densities.
Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB)
terms due to the exciton-exciton interaction and the kinetics of the anomalous
functions F_k= <a_k a_{-k}>. The collision terms are analyzed and an
approximation is used which is consistent with the existence of BEC. The
inclusion of the coherent x-x interaction does not change the dephasing laws.
The anomalous function F_k exhibits a clear threshold behaviour at the critical
density.
