  In this paper we are interested in understanding the impact of surface
defects on a condensate of electron pairs in a quantum wire. Based on previous
results we establish a simple mathematical model in order to account for such
surface effects. For a system of non-interacting pairs, we will prove the
destruction of the condensate in the bulk. Finally, taking repulsive
interactions between the pairs into account, we will show that the condensate
is recovered for pair densities larger than a critical one given the number of
the surface defects is not too large.
