Quantum Aging in Mean-Field Models

We study the real-time dynamics of quantum models with long-range interactions coupled to a heat bath within the closed-time path-integral formalism. We show that quantum fluctuations depress the transition temperature. In the subcritical region there are two asymptotic time regimes with (i) stationary and (ii) slow aging dynamics. We extend the quantum fluctuation-dissipation theorem to the nonequilibrium case in a consistent way with the notion of an effective temperature that drives the system in the aging regime. The classical results are recovered for $ħ\to 0$.