Out-of-equilibrium chiral condensate in AdS/QCD

We study the chiral condensate at finite temperature in AdS/QCD in a time-dependent background, in which the position of the black-hole horizon $z_h$ changes with time, producing an increasing or decreasing temperature. Conformal invariance is broken, as in the soft-wall model, by a static quadratic dilaton. Two different scenarios are analysed: in the first a general power-law time dependence is assumed for $z_h$, while in the second the energy-momentum tensor at late times reproduces the one found in viscous hydrodynamics. Depending on the rate at which the system evolves, the transition shifts toward lower temperatures. If the chiral condensate is far from equilibrium at low temperatures, oscillations around its equilibrium value are observed before thermalization. A prethermalization stage is found in the chiral limit if the initial condition is set at a temperature close to the critical one. In the hydrodynamic setup the evolution of the medium is slow enough, and the chiral condensate soon matches the equilibrium curve.