On the Bardeen-Cooper-Schrieffer interaction in quantum graphs

TL;DR

This paper develops a real-space BCS interaction model on quantum graphs, revealing how network topology influences two-particle bound states and many-body pairing, with potential experimental implications.

Contribution

It introduces a real-space BCS interaction framework on quantum graphs and analyzes the effects of topology on pairing and bound states, supported by exact solutions.

Findings

Two-particle bound states are stabilized by graph topology.

Many-body effects do not diminish the pairing enhancement.

Experimental relevance to Josephson junction arrays is discussed.

Abstract

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 Schr\"{o}dinger equation. The solution of the two-body eigenproblem shows the presence of a two-particle bound state whose stability is enhanced in quantum graphs with peculiar network 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 peculiar connectivity. Experimental evidences in Josephson junctions arrays are also discussed in connection with the microscopic mechanism described in the present work.