Real-time nonequilibrium dynamics of quantum glassy systems

Abstract

We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral 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 an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model 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 critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely aging, survives the quantum fluctuations. In the sub-critical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin-glasses and the relevance of the effective temperatures with respect to the understanding of the low temperature dynamics.

Dynamical study of the disordered quantump=2spherical model

“…In this paper a motivating question is whether the introduction of quantum fluctuations in a classical system out of equilibrium results in qualitatively new behavior at long time-scales. To date, the introduction of quantum fluctuations in theoretical glassy models has not led to qualitative changes, e.g., new slow quantum modes, in their long-time dynamics [1,2,3,4,5]. Quantum fluctuations often drive the glass transition to be first-order [6,7,8,9,10], and thus only qualitatively affect the dynamical behavior on short-time scales.…”

Coarsening of disordered quantum rotors under a bias voltage

“…11. The relations between integrated responses and correlation functions in other quantum problems that also approach classical-like form in the aging regime were shown in [31,37].…”

“…Finally, as a consequence of its disordered interactions, the system of rotors experiences intrinsic difficulties to reach equilibrium. Indeed, even if it were embedded within an equilibrium environment it would show a glassy phase [29,31] in some parts of the phase diagram.…”

“…This property allows us to write dynamic equations by averaging over disorder the generating functional itself hence without resorting to the use of replicas [31]. As in other quantum systems with quenched disorder [29,31,35,37], we are therefore interested in…”

“…Moreover the connection with the Martin-Siggia-Rose generating functional in the classical limit is more straightforward in this representation [26,31]. One introduces new fields as 31) and the inversion relation…”