  We study the long time dynamics of quantum spin glasses of rotors using the
non-equilibrium Schwinger-Keldysh formalism. These models are known to have a
quantum phase transition from a paramagnetic to a spin glass phase, which we
approach by looking at the divergence of the spin relaxation rate at the
transition point. In the aging regime, we determine the dynamical equations
governing the time evolution of the spin response and correlation functions,
and show that all terms in the equations that arise solely from quantum effects
are irrelevant at long times under time reparametrization group (RpG)
transformations. At long times, quantum effects enter only through the
renormalization of the parameters in the dynamical equations for the classical
counterpart of the rotor model. Consequently, quantum effects only modify the
out of equilibrium fluctuation dissipation relation (OEFDR), i.e. the ratio X
between the temperature and the effective temperature, but not the form of the
classical OEFDR.
