Thermalization of Green functions and quasinormal modes

TL;DR

This paper introduces a new method to analyze the thermalization process of Green functions in holographic conformal field theories, revealing that late-time behavior is governed by quasinormal modes and applying it to various AdS Vaidya models.

Contribution

The paper develops an analytic and numerical method based on derivatives at the shell to study Green function thermalization in holography, connecting late-time behavior to quasinormal modes.

Findings

Late-time Green function behavior is determined by the first quasinormal mode.

The method successfully describes thermalization in AdS3 and AdS5 Vaidya geometries.

Universal shear viscosity to entropy density ratio is obtained from a time-dependent process.

Abstract

We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the first quasinormal mode. We then implement the method numerically. As applications of this method we study the thermalization of the retarded time dependent Green function corresponding to a minimally coupled scalar in the AdS3 and AdS5 thin Vaidya shells. We see that as expected the late time behaviour is determined by the first quasinormal mode. We apply the method to study the late time behaviour of the shear vector mode in AdS5 Vaidya shell. At small momentum the corresponding time dependent Green function is expected to relax to equilibrium by the shear hydrodynamic mode. Using this we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.