  Emission spectra of quantum dot arrays in zero-dimensional microcavities are
studied theoretically, and it is shown that they are determined by the
competition between the formation of the collective superradiant mode and
inhomogeneous broadening. The random sources method for the calculation of
photoluminescence spectra under a non-resonant pumping is developed, and a
microscopic justification of the random sources method within a framework of
the standard diagram technique is given. The emission spectra of a microcavity
are analyzed with allowance for the spread of exciton states energies caused by
an inhomogeneous distribution of quantum dots and a tunneling between them. It
is demonstrated that in the case of a strong tunneling coupling the
luminescence spectra are sensitive to the geometric positions of the dots, and
the collective mode can, under certain conditions, be stabilized by the random
tunnel junctions.
