Abstract
We studied the evolution of the Wightman correlator in a thermalizing state modeled by ${\mathrm{AdS}}_{3}$-Vaidya background. We gave a prescription for calculating the Wightman correlator in coordinate space without using any approximation. For equal-time correlator $⟨O(v,x)O(v,0)⟩$, we obtained an enhancement factor ${v}^{2}$ due to long range correlation present in the initial state. This was missed by previous studies based on geodesic approximation. We found that the long range correlation in initial state does not lead to significant modification to thermalization time as compared to known results with generic initial state. We also studied the spatially integrated Wightman correlator and showed evidence on the distinction between long distance and small momentum physics for an out-of-equilibrium state. We also calculated the radiation spectrum of particles weakly coupled to $O$ and found that lower frequency mode approaches thermal spectrum faster than high frequency mode.
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