Instantaneous Thermalization in Holographic Plasmas

Thin-shell AdS-Vaidya spacetimes can be considered as holographic models of the thermalization process in strongly-coupled conformal field theories following a rapid injection of energy from an external source. While the expected thermalization time is the inverse temperature, Bhattacharyya and Minwalla have pointed out that bulk causality implies that expectation values of local field-theory observables actually take on their thermal values immediately following the injection. In this paper we study two-point functions, for which the causality argument does not apply. Specifically, we study the Brownian motion of a "quark" represented by a string stretching from the boundary to the horizon of an AdS_3-Vaidya spacetime. Surprisingly, we find that the two-point function also thermalizes instantly. Since Brownian motion is a 1/N effect, our result shows that, at least in certain cases, the rapid thermalization property of holographic plasmas persists beyond leading order in 1/N.