Holographic thermalization with initial long range correlation

TL;DR

This paper investigates the evolution of Wightman correlators during thermalization in a holographic model, revealing the impact of initial long-range correlations and distinguishing between long-distance and small-momentum physics.

Contribution

It provides a new prescription for calculating Wightman correlators without approximation and highlights the effects of initial long-range correlations on thermalization dynamics.

Findings

Long-range correlations enhance equal-time correlators by a factor of v^2.

Long-range correlations do not significantly alter thermalization time.

Lower frequency modes approach thermal equilibrium faster than high frequency modes.

Abstract

We studied the evolution of Wightman correlator in a thermalizing state modeled by AdS_3-Vaidya background. We gave a prescription for calculating Wightman correlator in coordinate space without using any approximation. For equal-time correlator $\langle O(v,x)O(v,0)\rangle$, 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 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 radiation spectrum of particle weakly coupled to $O$ and found lower frequency mode approaches thermal spectrum faster than high frequency mode.