  In this work, we present a theoretical study of a quantum dot-microcavity
system which includes a constant magnetic field in the growth direction of the
micropillar. First, we study the zero temperature case by means of a
selfconsistent procedure with a trial function composed by a coherent photon
field and a BCS function for the electron-hole pairs. The dependence of the
ground-state energy on the magnetic field and the number of polaritons is
found. We show that the magnetic field can be used as a control parameter of
the photon number, and we make explicit the scaling of the total energy with
the number of polaritons. Next, we study this problem at finite temperatures
and obtain the scaling of the critical temperature with the number of
polaritons.
