Generalized Wick's theorem for multiquasiparticle overlaps as a limit of Gaudin's theorem

By using the extension of the statistical Wick's theorem (Gaudin's theorem) to deal with generalized statistical density operators (those which can be expressed as the product of and operator carrying out a canonical transformations times a density operator) and using the appropriate limits we are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean-field wave functions. Due to the simplicity of the derivation it is now straightforward to consider more involved cases and some of them are discussed. The present derivation also allows us to obtain general and compact formulas for other particular cases of the generalized Wick theorem involving overlaps of multiquasiparticle excitations of product wave functions. The new expressions allow us to reduce the combinatorial complexity of the standard calculation of the above overlaps.