量子图中的Bardeen-Cooper-Schrieffer相互作用研究
On the Bardeen-Cooper-Schrieffer interaction in quantum graphs
AI总结：
本文在量子图中引入实空间Bardeen-Cooper-Schrieffer相互作用，发现特殊网络拓扑可增强两粒子束缚态稳定性，且该增强对多体效应具有鲁棒性，为理解Josephson结阵列中的有效配对增强提供了微观机制。
摘要：
我们引入了一种实空间版本的Bardeen-Cooper-Schrieffer相互作用，从而能够研究量子图上多体物理与粒子约束之间非平凡的相互作用。在考虑两体问题时，我们发现两粒子波函数是一个积分-微分薛定谔方程的解。两体本征问题的解表明存在一个两粒子束缚态，其稳定性在具有特殊网络拓扑的量子图中得到增强。我们证明这种增强效应对多体效应具有鲁棒性，而多体效应可以通过Richardson精确解来研究。这些发现表明，在具有特殊连通性的量子图中，有效配对相互作用可以得到增强。本文还讨论了Josephson结阵列中的实验证据，并将其与本文所描述的微观机制联系起来。
英文摘要：
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 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.
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