How do initial conditions influence the evolution of correlations in a non-equilibrium system?*

A key problem in describing the dynamics of an interacting system starting from initial states with non-trivial connected correlations is that Wick's theorem is no longer valid in this system. We show that Wick's theorem and resultant other structures of interacting field theories can be restored in such a situation for fermions if one considers additional interaction vertices related to the initial correlations. We use this to study how the evolution of one particle correlations in a Hubbard model is affected by initial correlations in the system.