Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems

摘要: The use of exactly solvable Richardson-Gaudin models to describe the physics systems with strong pair correlations is reviewed. article begins a brief discussion Richardson's early work, which demonstrated exact solvability pure pairing model, and then shows how that work has evolved recently into much richer class models. Richardson solution leads naturally an analogy between these quantum classical electrostatic problems in two dimensions. This used demonstrate formally BCS theory emerges as large-$N$ limit Hamiltonian. Several applications relevance condensed-matter physics, nuclear confined are considered. Some interesting effects discussed context include (i) crossover from superconductivity fluctuation-dominated regime small metallic grains; (ii) role nucleon Pauli principle suppressing high-spin bosons interacting boson nuclei, (iii) possibility fragmentation systems. Interesting insight also provided origin superconducting phase transition both two-dimensional electronic atomic based on image corresponding