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Precision studies of v_n fluctuations

The power spectrum of heavy ion collisions is investigated by studying initial state fluctuations on top of a smooth hydrodynamic flow. In particular, the stability of the location of the first minimum of the power spectrum and the dependence of the hydrodynamic response v_n / epsilon_n on n and on eta / s are discussed. In our study we develop a new Green's function method for the analytic hydrodynamic flow by S. Gubser and make use of a fully non-linear hydrodynamics code. We find that there will be no well-defined first minimum of the response for n < 10, due to the fact that all minima in that region are found to be sensitive to the location of the initial perturbations. Also, we find that the often proposed form of the hydrodynamical response, that ln ( v_n / epsilon_n ) depend quadratically on n and linearly on eta / s, should not hold once many events have been averaged over.