The power spectrum of cosmic ray arrival directions

Various experiments show that the arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It was recently argued that this small scale structure may arise naturally by cosmic ray diffusion in a large-scale cosmic ray gradient in combination with deflections in local turbulent magnetic fields. We show via analytical and numerical methods that the non-trivial power spectrum in this setup is a direct consequence of Liouville's theorem and can be related to properties of relative diffusion.