Fluctuation and dissipation within a deformed holographic model with backreaction

TL;DR

This paper investigates fluctuation and dissipation phenomena in a deformed holographic model with backreaction, computing key physical quantities and confirming the fluctuation-dissipation theorem within this modified AdS-Schwarzschild spacetime.

Contribution

It introduces a novel holographic model with exponential warp factor backreaction and analyzes fluctuation and dissipation properties in this setup.

Findings

Computed admittance, diffusion coefficient, and two-point functions.

Confirmed fluctuation-dissipation theorem in the deformed model.

Identified Brownian motion regimes from mean square displacement.

Abstract

In this work we study the fluctuation and dissipation of a string attached to a brane in a deformed and backreated AdS-Schwarzschild spacetime. This space is a solution of Einstein-dilaton equations and contains a conformal exponential factor $\exp(k/r^2)$ in the metric. We consider the backreaction contributions coming only from the exponential warp factor on the AdS-Schwarzschild black hole, where the string and brane are in the probe approximation. Within this Lorentz invariant holographic model we have computed the admittance, the diffusion coefficient, the two-point functions and the regularized mean square displacement $s^2_{reg}$. From this quantity we obtain the diffuse and ballistic regimes characteristic of the Brownian motion. From the two-point functions and the admittance, we also have checked the well know fluctuation-dissipation theorem in this set up.