  A nano-system in which electrons interact and in contact with Fermi leads
gives rise to an effective one-body scattering which depends on the presence of
other scatterers in the attached leads. This non local effect is a pure
many-body effect that one neglects when one takes non interacting models for
describing quantum transport. This enhances the non-local character of the
quantum conductance by exchange interactions of a type similar to the
RKKY-interaction between local magnetic moments. A theoretical study of this
effect is given assuming the Hartree-Fock approximation for spinless fermions
in an infinite chain embedding two scatterers separated by a segment of length
L\_c. The fermions interact only inside the two scatterers. The dependence of
one scatterer onto the other exhibits oscillations which decay as 1/L\_c and
which are suppressed when L\_c exceeds the thermal length L\_T. The
Hartree-Fock results are compared with exact numerical results obtained with
the embedding method and the DMRG algorithm.
