and search for the Fourier transform of it, remembering that the Fourier transform of a Lorentzian line shape is producing a time correlation function which is an exponential decay over time, and that, in the case of the Gaussian line shape, we have a correlation with is a Gaussian function of time. Being the q-Gaussian a line shape which is intermediate between Lorentzian and Gaussian profiles, the related time correlation function must be intermediate between the exponential decay over time and a Gaussian function.