  We set the formalism to study the way in which the choice of canonical
equilibrium initial conditions affect the real-time dynamics of quantum
disordered models. We use a path integral formulation on a time contour with
real and imaginary time branches. The factorisation of the time-integration
paths usually assumed in field-theoretical studies breaks down due to the
averaging over quenched randomness. We derive the set of Schwinger-Dyson
dynamical equations that govern the evolution of linear response and
correlation functions. The solution of these equations is not straightforward
as it needs, as an input, the full imaginary-time (or Matsubara frequency)
dependence of the correlation in equilibrium. We check some limiting cases
(equilibrium dynamics, classical limit) and we set the stage for the analytic
and numerical analysis of quenches in random quantum systems.
