Anisotropic flows and the shear viscosity of the QGP within an event by event transport approach

We study the effect of a temperature dependent shear viscosity to entropy density ratio eta/s(T) on the build-up of the anisotropic flows v(n)(p(T)) within a relativistic kinetic transport approach that incorporates initial state fluctuations. We find that only in ultra-central collisions (0 - 0.2%) the v(n)(p(T)) have a stronger sensitivity to the T dependence of eta/s in the QGP phase and this sensitivity increases with the order of the harmonic n. We study the linear correlation coefficient C(epsilon(n),v(n)) for different impact parameters and for two different beam energies: Au+Au at root s = 200 GeV at RHIC and Pb + Pb at root S = 2.76 T eV at LHC. The study of the correlations shows that at LHC energies there is more correlation than at RHIC energies. At LHC energies and for ultra-central collisions the linear correlation coefficient C(epsilon(n), v(n)) approximate to 1 for n = 2, 3, 4 and 5.