  We present numerical results for electron spin relaxation rates for single
and laterally coupled double GaAs quantum dots in a perpendicular magnetic
field. As source of spin relaxation we consider hyperfine interaction with the
nuclear spins in the GaAs substrate. Due to the differences in the energy
scales of the nuclear and electronic Zeeman energies, the phonon bath system
has to be taken into account for energy dissipation. The corresponding
transition rates of second order show strong dependencies on correlations
between the electrons and the electronic energy differences, and hence on the
magnetic field. For a highly asymmetric double dot we have found a relatively
low second order electron spin relaxation rate for a wide range of magnetic
fields.
