Dynamics of holographic thermalization

TL;DR

This paper investigates the dynamics of thin shells collapsing in asymptotically AdS spaces to understand holographic thermalization in strongly coupled systems, analyzing different matter types and space-time dimensions through minimal surface probes.

Contribution

It provides a comprehensive study of thermalization timescales for various shell matter types and differing cosmological constants, extending previous models like AdS-Vaidya.

Findings

Conformal matter shells lead to significantly longer thermalization times.

Scalar field shells collapse only when inner and outer cosmological constants differ.

Thermalization times vary with matter type and space-time dimensions.

Abstract

Dynamical evolution of thin shells composed by different kinds of degrees of freedom collapsing within asymptotically AdS spaces is explored with the aim of investigating models of holographic thermalization of strongly coupled systems. From the quantum field theory point of view this corresponds to considering different thermal quenches. We carry out a general study of the thermalization time scale using different parameters and space-time dimensions, by calculating renormalized space-like geodesic lengths and rectangular minimal area surfaces as extended probes of thermalization, which are dual to two-point functions and rectangular Wilson loops. Different kinds of degrees of freedom in the shell are described by their corresponding equations of state. We consider a scalar field, as well as relativistic matter, a pressureless massive fluid and conformal matter, which can be compared with the collapse of an AdS-Vaidya thin shell. Remarkably, for conformal matter, the thermalization time scale becomes much larger than the others. Furthermore, in each case we also investigate models where the cosmological constants of the inner and outer regions separated by the shell are different. We found that in this case only a scalar field shell collapses, and that the thermalization time scale is also much larger than the AdS-Vaidya case.