Cooper-pair transport through a Hubbard chain sandwiched between two   superconductors: Density matrix renormalization group calculations
  We present a numerical approach to study the coherent transport of Cooper pairs through a Hubbard chain, and study the role of the contacts in achieving perfect Andreev reflection. We calculate the pair transport using the Density Matrix Renormalization Group by measuring the response of the system to quantum pair fields with complex phases on the two ends of an open system. This approach gives an effective superfluid weight which is in close agreement with the Bethe Ansatz results for the superfluid weight for closed Hubbard rings. 
A. E. Feiguin, S. R. White, D. J. Scalapino