https://doi.org/10.1140/epjp/s13360-023-04054-6
Regular Article
On the Bardeen–Cooper–Schrieffer interaction in quantum graphs
1
Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno, Via Giovanni Paolo II, 84084, Fisciano, SA, Italy
2
INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Via Giovanni Paolo II, 84084, Fisciano, SA, Italy
Received:
25
January
2023
Accepted:
2
May
2023
Published online:
26
May
2023
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 Schrödinger 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.
© The Author(s) 2023
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