Exact relations for a strongly corelated Fermi gas and a novel mathematical method

Two-component ultracold atomic Fermi gases with large scattering lengths are important strongly-correclated many-body systems. Their properties are difficult to predict, expecially in the interesting case of imbalanced populations. It is shown that one can netertheless derive several universal exact relations, exploiting the fact that the range of the interaction is short. A novel mathematical technique is used to make the derivation of these results easier.