Evolution of Two-Point Functions from Holography

TL;DR

This paper investigates the evolution of two-point functions during thermalization in a 2D holographic CFT, revealing how quantum correlations influence equilibration and the late-time behavior of correlations.

Contribution

It provides a holographic analysis of two-point function dynamics during thermalization, highlighting the role of initial quantum correlations and the effective distance dependence at late times.

Findings

Equilibration occurs only within finite regions growing with time.

Late-time two-point functions depend on the effective distance l - t1 - t2.

Initial quantum correlations significantly affect the thermalization process.

Abstract

We consider a thermalization process in a 2-dimensional CFT that has a holographic description in terms of the gravitational collapse of a thin shell of null dust. This model represents a sudden perturbation of the CFT vacuum that communicates a uniform energy density to the system. We study the evolution of two-point functions at spacelike separated points (t1,l) and (t2,0), and reproduce the generic pattern first derived from the analysis of quantum quenches to critical systems. A crucial characteristic of these setups is that the excitations generated by the initial perturbation presents non-trivial quantum correlations. As a consequence, for any ti<infinity equilibration is only effective on finite regions whose size grows as a lightfront. The behavior on larger regions is greatly determined by the initial state, which for the quenches we consider and the holographic model has relevant differences. However in both cases for late times the dependence on the scale l of the two-point functions enters through the effective distance l-t1-t2. We interpret the onset of this behavior as an equilibration time for occupation numbers in these 2-dimensional models.