Abstract
In this work we study the fluctuation and dissipation of a string attached to a brane in a deformed and backreacted AdS-Schwarzschild spacetime. This space is a solution of Einstein-dilaton equations and contains a conformal exponential factor exp(k/r2) 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 sreg2. 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.
Highlights
Brownian motion [1, 2] and the fluctuation-dissipation theorem [3] stand until today as two of the most important subjects within non-equilibrium statistical mechanics
A very interesting approach to deal with non-perturbative aspects of strong interactions, which appear in such processes, is based on the AdS/CFT correspondence [6] which relates a weak coupled theory in a curved spacetime (AdS5) with a strong coupled theory in four dimensional Minkowski spacetime
In this work, taking into account a conformal exponential factor exp(k/r2) and the horizon function obtained from the solutions of Einstein-dilaton equations we have constructed a deformed and backreacted Lorentz invariant holographic model
Summary
Brownian motion [1, 2] and the fluctuation-dissipation theorem [3] stand until today as two of the most important subjects within non-equilibrium statistical mechanics. This deformation is due to the introduction of a conformal factor exp(k/r2) in the metric of such a space They computed the string energy, the response function, the mean square displacement, the diffusion coefficient and checked the fluctuation-dissipation theorem. This and related deformed AdS/QCD models were used successfully in many holographic problems as can be seen, for example, in Refs. In this work we will use a probe string attached to a probe brane in a Lorentz invariant deformed AdS/QCD model taking into account the backreaction from the exponential factor on the metric of the AdS-Schwarzschild space This will allow us to extend the work done in Ref.
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