Holographic RG Flow and Sound Modes of sQGP

We consider the hydrodynamics of strongly interacting quark gluon plasma in finite temperature and density using the holographic duality of charged black hole in anti DeSitter space. We calculate the transport coefficients at arbitrary energy scale by considering the holographic screen at finite radial position. We first calculate the flow of sound velocity in this method and check the consistence with previous result. Then we calculate diffusion constant of charge and find that Einstein relation between susceptibility, conductivity and diffusion constant will hold at arbitrary slice.