  We have studied the dissipative dynamics of a driven electronic spin trapped
in a quantum dot. We consider the dissipative mechanism as due to the indirect
coupling of the electronic spin to acoustic phonons via the
spin-orbit/electron-phonon couplings. Using an effective spectral function of
the dissipative phonon bath, we evaluated the expectation values of the spin
components through the Bloch-Redfield theory. We show that due to a sharp bath
resonance present in the effective spectral function, with typical energy much
smaller than the electronic confinement energy, the dissipative spin has a rich
dynamical behavior that helps us to determine some features of the spin-bath
coupling. We also quantify the effects produced by the sharp bath resonance,
and thus indicate the best regimes of operation in order to achieve the longest
relaxation times for the spin.
