Exactly solvable Richardson–Gaudin models and their applications

Abstract

We first show that the quantum pairing problem can be mapped exactly on to a classical electrostatic problem in two dimensions and then use this analogy to obtain a pictorial representation of how superconductivity arises in a finite fermionic system. Specific application to the nuclei 114−116Sn suggests some new insight into the evolution of pairing correlations in a quantum system with few active particles. We also summarize other recent work on exactly solvable pairing models, including their applications in a wide variety of strongly correlated quantum systems.