  We present a theoretical study of the collective optical effects which can
occur in groups of three and four quantum dots. We define conditions for stable
subradiant (dark) states, rapidly decaying superradiant states,and spontaneous
trapping of excitation. Each quantum dot is treated like a two-level system.
The quantum dots are though realistic, meaning that they may have different
transition energies and dipole moments. The dots interact via a short-range
coupling which allows excitation transfer across the dots, but conserves the
total population. We calculate the time evolution of single- and biexciton
states using the Linblad equation. In the steady state the individual
populations of each dot may have permanent oscillations with frequencies given
by the energy separation between the subradiant eigenstates.
