Holographic Thermalization in Charged Dilaton Anti-de Sitter Spacetime

TL;DR

This paper investigates how chemical potential and dilaton coupling influence holographic thermalization times in charged AdS spacetimes, revealing a universal saturation time behavior despite complex dependencies.

Contribution

It introduces a detailed analysis of the effects of chemical potential and dilaton coupling on holographic thermalization, highlighting the near-universality of saturation time across different parameters.

Findings

Saturation time is not always monotonically related to chemical potential ratio.

The effect of dilaton coupling on thermalization depends on its value, with different behaviors for $ ext{0} \\leq \\alpha \\leq 1$ and $\\alpha > 1$.

Saturation time shows universality, being nearly unaffected by the dilaton-Maxwell coupling constant.

Abstract

We study holographic thermalization in spacetimes with a chemical potential and a non-trivial dilaton field. Three non-local observables are used to probe the whole process and investigate the effect of the ratio of the chemical potential over temperature $\chi$ and the dilaton-Maxwell coupling constant $\alpha$. It is found that the saturation time is not always a monotonically increasing function of $\chi$, the situation depends on $\alpha$. When $0 \leq\alpha \leq 1$, larger $\chi$ yields longer saturation time, while for $\alpha>1$, the situation becomes more complex. More interesting, we found that although $\alpha$ indeed has influence on the whole thermalization process, it nearly does not affect the saturation time, which indicates the universality of the saturation time for the dual one-parameter field theories.