Fermionic and bosonic fluctuation-dissipation theorem from a deformed AdS holographic model at finite temperature and chemical potential

TL;DR

This paper investigates fluctuation and dissipation phenomena in a deformed AdS holographic model at finite temperature and chemical potential, deriving fluctuation-dissipation relations for bosonic and fermionic systems.

Contribution

It introduces a deformed AdS black hole model with backreaction effects and computes fluctuation-dissipation relations for both bosonic and fermionic fluctuations.

Findings

Derived admittance dependence on temperature and chemical potential.

Calculated two-point correlation functions and mean square displacement.

Confirmed fluctuation-dissipation theorem for bosonic and fermionic cases.

Abstract

In this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein-Maxwell-Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases, from which we obtain the short and large time approximations. For the long time, we obtain a sub-diffusive regime $\sim \log t$. Combining the results from the admittance and the correlations functions we check the fluctuation-dissipation theorem for bosonic and fermionic systems.