  We develop a systematic analytic approach to aging effects in quantum
disordered systems in contact with an environment. Within the closed-time
path-integral formalism we include dissipation by coupling the system to a set
of independent harmonic oscillators that mimic a quantum thermal bath. After
integrating over the bath variables and averaging over disorder we obtain an
effective action that determines the real-time dynamics of the system. The
classical limit yields the Martin-Siggia-Rose generating functional associated
to a colored noise. We apply this general formalism to a prototype model
related to the $p$ spin-glass. We show that the model has a dynamic phase
transition separating the paramagnetic from the spin-glass phase and that
quantum fluctuations depress the transition temperature until a quantum
critical point is reached. We show that the dynamics in the paramagnetic phase
is stationary but presents an interesting crossover from a region controlled by
the classical critical point to another one controlled by the quantum critical
point. The most characteristic property of the dynamics in a glassy phase,
namely aging, survives the quantum fluctuations. In the sub-critical region the
quantum fluctuation-dissipation theorem is modified in a way that is consistent
with the notion of effective temperatures introduced for the classical case. We
discuss these results in connection with recent experiments in dipolar quantum
spin-glasses and the relevance of the effective temperatures with respect to
the understanding of the low temperature dynamics.
