Real-time nonequilibrium dynamics of quantum glassy systems

We develop a systematic analytic approach to aging effects in quantum disor dered systems in contact with an environment. Within the closed-time path-i ntegral 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 a n effective action that determines the real-time dynamics of the system. Th e classical limit yields the Martin-Siggia-Rose generating functional assoc iated to a colored noise. We apply this general formalism to a prototype mo del 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 cri tical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controll ed by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glas sy phase, namely, aging, survives the quantum fluctuations. In the subcriti cal region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced fo r the classical case. We discuss these results in connection with recent ex periments in dipolar quantum spin glasses and the relevance of the effectiv e temperatures with respect to the understanding of the low-temperature dyn amics. [S0163-1829(99)14001-3].