  We use the Bloch-Redfield-Wangsness theory to calculate the effects of
acoustic phonons in coherent control experiments, where quantum-dot excitons
are driven by shaped laser pulses. This theory yields a generalized Lindblad
equation for the density operator of the dot, with time-dependent damping and
decoherence due to phonon transitions between the instantaneous dressed states.
It captures similar physics to the form recently applied to Rabi oscillation
experiments [A. J. Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)], but
guarantees positivity of the density operator. At sufficiently low
temperatures, it gives results equivalent to those of fully non-Markovian
approaches [S. Luker et al., Phys. Rev. B 85, 121302 (2012)], but is
significantly simpler to simulate. Several applications of this theory are
discussed. We apply it to adiabatic rapid passage experiments, and show how the
pulses can be shaped to maximize the probability of creating a single exciton
using a frequency-swept laser pulse. We also use this theory to propose and
analyze methods to determine the phonon density of states experimentally, i.e.
phonon spectroscopy, by exploring the dependence of the effective damping rates
on the driving field.
