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Initial state fluctuations from mid-peripheral to ultra-central collisions in a event-by-event transport approach

We have developed a relativistic kinetic transport approach that incorporates initial state fluctuations allowing to study the build up of elliptic flow $v_2$ and high order harmonics $v_3$, $v_4$ and $v_5$ for a fluid at fixed $η/s(T)$. We study the effect of the $η/s$ ratio and its T dependence on the build up of the $v_n(p_T)$ for two different beam energies: RHIC for Au+Au at $\sqrt{s}=200 \,GeV$ and LHC for $Pb+Pb$ at $\sqrt{s}=2.76 \,TeV$. We find that for the two different beam energies considered the suppression of the $v_n(p_T)$ due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. Our study reveals that only in ultra-central collisions ($0 - 0.2 \%$) the $v_n(p_T)$ have a stronger sensitivity to the T dependence of $η/s$ in the QGP phase and this sensitivity increases with the order of the harmonic n. Moreover, the study of the correlations between the initial spatial anisotropies $ε_n$ and the final flow coefficients $v_n$ shows that at LHC energies there is more correlation than at RHIC energies. The degree of correlation increases from peripheral to central collisions, but only in ultra-central collisions at LHC, we find that the linear correlation coefficient $C(n,n) \approx 1$ for $n=2,3,4$ and $5$. This suggests that the final correlations in the ($v_n$,$v_m$) space reflect the initial correlations in the ($ε_n$,$ε_m$) space.