An extended Vlasov equation with pairing correlations
  A simplified version of the Wigner--transformed time--dependent Hartree--Fock--Bogoliubov equations, leading to a solvable model for finite systems of fermions with pairing correlations, is introduced. In this model, pairing correlations result in a coupling of the Vlasov--type equation for the normal phase--space density with that for the imaginary part of the anomalous density. The effect of pairing correlations on the linear response of the system is studied for a finite one--dimensional system and an explicit expression for the correlated propagator is given. 
V. I. Abrosimov (1), D. M. Brink (2), A. Dellafiore (3 and 4), F.   Matera (3 and 4) ((1) Institute for Nuclear Research, Ki...