  Multiphonon processes in a model quantum dot (QD) containing two electronic
states and several optical phonon modes are considered taking into account both
intra- and inter-level terms. The Hamiltonian is exactly diagonalized including
a finite number of multi-phonon processes, large enough as to guarantee that
the result can be considered exact in the physically important region of
energies. The physical properties are studied by calculating the electronic
Green's function and the QD dielectric function. When both the intra- and
inter-level interactions are included, the calculated spectra allow for
explanation of several previously published experimental results obtained for
spherical and self-assembled QDs, such as enhanced 2LO phonon replica in
absorption spectra and up-converted photoluminescence. An explicit calculation
of the spectral line shape due to intra-level interaction with a continuum of
acoustic phonons is presented, where the multi-phonon processes also are shown
to be important. It is pointed out that such an interaction, under certain
conditions, can lead to relaxation in the otherwise stationary polaron system.
