Holograghic Brownian motion in three dimensional G\"{o}del black hole

By using the AdS/CFT correspondence and G\"{o}del black hole background, we study the dynamics of heavy quark under a rotating plasma. In that case we follow Atmaja (JHEP 1304, 021, (2013)) about Brownian motion in BTZ black hole. In this paper we receive some new results for the case of $\alpha^{2}l^{2}\neq1$. This case, we must redefine the angular velocity of string fluctuation. We obtain the time evolution of displacement square that angular velocity and show that it behaves as a Brownian particle in non-relativistic limit. In this plasma, it seems that relating the Brownian motion with physical observables is rather a difficult work. But our results match with Atmaja work in the limit $\alpha^{2}l^{2}\rightarrow1$.Comment: 16 page

Holograghic Brownian motion in 2+12+1 dimensional hairy black holes

In this paper, we investigate the dynamics of a heavy quark under the plasmas correspond to three dimensional hairy black holes. We utilize the AdS/CFT correspondence to study the holographic Brownian motion of this particle in different kinds of hairy black holes. For uncharged black hole at low frequency limit we derive analytic expressions for correlation functions and response functions and verify that the fluctuation-dissipation theorem holds in the presence of a scalar field in the metric background. In the case of charged black hole, we think that the results are similar to what derived for uncharged black hole.Comment: 15 page