Theory of mesoscopic magnetism in meta-materials

We provide a rigorous theoretical basis for the artificial magnetic activity of meta-materials near resonances. Our approach is a renormalization-based scheme that authorises a completely general theory. The major result is an explicit expression of the effective permeability, in terms of resonant frequencies. The theoretical results are checked numerically and we give applications of our theory to Left-Handed Media and to the solution of the Pokrovski-Efros paradox.