Abstract
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.