Impact of surface defects on a condensate of electron pairs in a quantum wire

We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical model accounting for such surface effects. For a system of noninteracting pairs, we prove the destruction of the condensate in the bulk. Finally, taking repulsive interactions between the pairs into account, we show that the condensate is recovered for pair densities greater than a critical density if the number of the surface defects is not too large.