Quantum quench and double trace couplings

We consider quantum quench by a time dependent double trace coupling in a strongly coupled large N field theory which has a gravity dual via the AdS/CFT correspondence. The bulk theory contains a self coupled neutral scalar field coupled to gravity with negative cosmological constant. We study the scalar dynamics in the probe approximation in two backgrounds: AdS soliton and AdS black brane. In either case we find that in equilibrium there is a critical phase transition at a negative value of the double trace coupling κ below which the scalar condenses. For a slowly varying homogeneous time dependent coupling crossing the critical point, we show that the dynamics in the critical region is dominated by a single mode of the bulk field. This mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads to Kibble Zurek type scaling behavior. For the AdS soliton the system is non-dissipative and has z = 1, while for the black brane one has dissipative z = 2 dynamics. We also discuss the features of a holographic model which would describe the non-equilibrium dynamics around quantum critical points with arbitrary dynamical critical exponent z and correlation length exponent ν. These analytical results are supported by direct numerical solutions.