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We develop a systematic analytic approach to aging effects in quantumdisordered systems in contact with an environment. Within the closed-timepath-integral formalism we include dissipation by coupling the system to a setof independent harmonic oscillators that mimic a quantum thermal bath. Afterintegrating over the bath variables and averaging over disorder we obtain aneffective action that determines the real-time dynamics of the system. Theclassical limit yields the Martin-Siggia-Rose generating functional associatedto a colored noise. We apply this general formalism to a prototype modelrelated to the $p$ spin-glass. We show that the model has a dynamic phasetransition separating the paramagnetic from the spin-glass phase and thatquantum fluctuations depress the transition temperature until a quantumcritical point is reached. We show that the dynamics in the paramagnetic phaseis stationary but presents an interesting crossover from a region controlled bythe classical critical point to another one controlled by the quantum criticalpoint. The most characteristic property of the dynamics in a glassy phase,namely aging, survives the quantum fluctuations. In the sub-critical region thequantum fluctuation-dissipation theorem is modified in a way that is consistentwith the notion of effective temperatures introduced for the classical case. Wediscuss these results in connection with recent experiments in dipolar quantumspin-glasses and the relevance of the effective temperatures with respect tothe understanding of the low temperature dynamics.Comment: 56 pages, Revtex, 17 figures include

Real-time nonequilibrium dynamics of quantum glassy systems