  We theoretically examine the effect of the magnetic field on the relaxation
process of the exciton-polariton toward the Bose-Einstein condensation in GaAs
quantum wells. As a result of the modification of the exciton's effective mass,
Rabi splitting, and dispersion, the relaxation rate of polaritons toward
condensation has been significantly modified. Using a continuous pumping, the
dynamics of total and condensated polariton versus magnetic field has been
clarified. It has been shown that for low-energy pumping, the condensation is
significantly reduced with a magnetic field, and this arises from the reduction
of the scattering rate between energy levels when the steepness of the
dispersion at higher energy is reduced. Increasing of pump energy together with
the magnetic field could lead to a more effective relaxation and a much higher
number of condensated polariton is obtained.
