  We calculate the photoluminescence spectrum of a single semiconductor quantum
dot strongly coupled to a continuum as a function of light frequency, gate
voltage, and magnetic field. The spectrum is dominated by the recombination of
several excitonic states which can be considered as quantum quenchs in which
the many-body nature of the system is suddenly changed between initial and
final states. This is associated with an Anderson orthogonality catastrophe
with a power-law singularity at the threshold. We explain the main features
observed experimentally in the region of stability of the trion $X^-$, the
neutral exciton $X^0$ and the gate voltage induced transition between them.
