Abstract
Abstract We use the AdS/CFT correspondence to study a thermally isolated conformal field theory in four dimensions which undergoes a repeated deformation by an external periodic time-dependent source coupled to an operator of dimension Δ. The initial state of the theory is taken to be at a finite temperature. We compute the energy dissipated in the system as a function of the frequency and of the dimension Δ of the perturbing operator. This is done in the linear response regime. In order to study the details of thermalization in the dual field theory, the leading-order backreaction on the AdS black brane metric is computed. The evolution of the event and the apparent horizons is monitored; the increase of area in each cycle coincides with the increase in the equilibrium entropy corresponding to the amount of energy dissipated. The time evolution of the entanglement entropy of a spherical region and that of the two-points function of a probe operator with a large dimension are also inspected; we find a delay in the thermalization of these quantities which is proportional to the size of the region which is being probed. Thus, the delay is more pronounced in the infrared. We comment on a possible transition in the time evolution of the energy fluctuations.
Highlights
Half, provide an interesting situation that is “midway” between the case of bounded and unbounded potentials
We use the AdS/conformal field theories (CFT) correspondence to study a thermally isolated conformal field theory in four dimensions which undergoes a repeated deformation by an external periodic time-dependent source coupled to an operator of dimension ∆
One can think of the periodic source ξ(t) as the vacuum expectation value (VEV) of some field interacting with the CFT
Summary
One of the main tools in studying the reaction of a medium to a weak perturbation which tends to drive it out of equilibrium is the linear response theory. Im GR(ω, 0), being an odd function of ω, is expected to generically start off as ω T ζ−1 This behavior will be confirmed in the numerical analysis of section 4. In the limit t0 → 0, they found by numerical analysis that the energy dissipated in the quench is a divergent quantity for ∆ ≥ 2, which scales as 1/t02∆−4 (as log 1/t0 for ∆ = 2). In the case of ζ > 0, the energy dissipated at small t0, corresponding to a very fast quench, scales as This is in agreement with the numerical result obtained in [22, 26]. In the case of ζ < 0 there is no divergence, so the energy dissipated in the process should approach a constant in the limit of a sudden quench. We will turn to the study of periodically driven strongly coupled systems with the aid of the AdS/CFT correspondence
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