On the Bardeen-Cooper-Schrieffer interaction in quantum graphs

We introduce a real-space version of the Bardeen-Cooper-Schrieffer interaction allowing the investigation of the non-trivial interplay between many-body physics and particles confinement on a quantum graph. When the two-body problem is considered, we find that the two-particle wavefunction is solution of an integro-differential Schrodinger equation. The solution of the two-body eigenproblem shows the presence of a two-particle bound state whose stability is enhanced in graphs with peculiar topology. We demonstrate that the enhancement effect is robust against many-body effects, which can be studied by means of the Richardson exact solution of the many-body problem. These findings suggest that the effective pairing interaction can be enhanced in quantum graphs with appropriate connectivity. Experimental evidences in Josephson junctions arrays are also discussed in connection with the microscopic mechanism described in the present work.

Automated summary

We propose a real-space version of the Bardeen-Cooper-Schrieffer interaction to investigate the interplay between many-body physics and particle confinement on a quantum graph. For the two-body problem, the two-particle wavefunction is found to satisfy an integro-differential Schrodinger equation. The solution reveals the existence of a stable bound state that is enhanced in graphs with specific topology. The enhancement effect is shown to be robust against many-body effects, as demonstrated by the Richardson exact solution. This suggests that effective pairing interaction can be enhanced in quantum graphs with appropriate connectivity. Experimental evidences in Josephson junctions arrays are discussed in connection with the microscopic mechanism described in this work.