  The population dynamics of single- and bi-exciton states in semiconductor
nanocrystals is modeled numerically in the presence of Coulomb coupling between
single- and two-exciton states and a dissipation channel in order to study the
transient bi-exciton population that occurs in an optically excited
semiconductor nanocrystal. The results show that the system evolution strongly
changes if the dissipation is included. In a certain range of parameters, the
growth of the exciton number (MEG process) is fast (on picosecond time scale)
and the following decay (Auger process) is much slower (hundreds of
picoseconds). In some cases, the maximum occupation of the bi-exciton state
increases when dissipation is included. The dynamics of an ensemble of
nanocrystals with a certain size dispersion is studied by averaging over the
energy of the bi-exciton state which can be different for each single
nanocrystal. The validity of Markov and secular approximation is also verified.
