Weak Field Collapse in AdS: Introducing a Charge Density

TL;DR

This paper investigates how a non-zero chemical potential influences the thermalization process in a strongly coupled gauge theory using a gravity dual, revealing that higher chemical potential shortens thermalization time.

Contribution

It introduces a perturbative gravity model to study the impact of chemical potential on thermalization in AdS/CFT, a novel approach in this context.

Findings

Thermalization time decreases with increasing chemical potential.

Constructed a perturbative solution interpolating between AdS black holes.

Analyzed entanglement entropy evolution during thermalization.

Abstract

We study the effect of a non-vanishing chemical potential on the thermalization time of a strongly coupled large $N_c$ gauge theory in $(2+1)$-dimensions, using a specific bottom-up gravity model in asymptotically AdS space. We first construct a perturbative solution to the gravity-equations, which dynamically interpolates between two AdS black hole backgrounds with different temperatures and chemical potentials, in a perturbative expansion of a bulk neutral scalar field. In the dual field theory, this corresponds to a quench dynamics by a marginal operator, where the corresponding coupling serves as the small parameter in which the perturbation is carried out. The evolution of non-local observables, such as the entanglement entropy, suggests that thermalization time decreases with increasing chemical potential. We also comment on the validity of our perturbative analysis.