论文标题
在量子图中的Bardeen-Cooper-Schrieffer相互作用上
On the Bardeen-Cooper-Schrieffer interaction in quantum graphs
论文作者
论文摘要
我们介绍了Bardeen-Cooper-Schrieffer相互作用的真实空间版本，允许研究量子图上多体物理学和颗粒限制之间的非平凡相互作用。当考虑两体问题时，我们发现两粒子波函数是整个差异schrödinger方程的解。两体征收特征问题的解决方案显示了存在一个两粒子结合状态，其在具有特殊网络拓扑的量子图中的稳定性增强了。我们证明，增强效应对多体效应是可靠的，可以通过理查森精确解决多体问题进行研究。这些发现表明，在具有特殊连接性的量子图中可以增强有效的配对相互作用。还讨论了与本工作中描述的微观机制有关的约瑟夫森连接阵列中的实验证据。
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.
