标题： 精确可解的理查森-高丁模型用于多体量子系统 显示英文标题

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

摘要： Richardson-Gaudin（R-G）模型精确可解的使用来描述具有强对关联系统的物理被回顾。 我们从理查森早期工作的简要讨论开始，该工作展示了纯配对模型的精确可解性，然后展示这项工作如何最近演变成一个更加丰富的精确可解模型类。 然后我们展示理查森解如何自然地引导出此类量子模型与二维经典静电问题之间的精确类比。 这随后被用来正式演示BCS理论是如何作为纯配对哈密顿量的大N极限出现，并且接着应用于与凝聚态物理、核物理以及受限系统相关的几个问题。 这些精确可解模型中讨论的一些有趣效应包括：（1）小金属颗粒中从超导性到波动主导区域的转变，（2）核子泡利原理在抑制相互作用玻色子模型中的高自旋玻色子影响方面的作用，以及（3）受限玻色子系统中碎裂的可能性。 基于相应精确可解量子配对模型的静电图像，还提供了关于二维电子系统和原子核中超导相变起源的有趣见解。 显示英文摘要

摘要： The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the physics of systems with strong pair correlations is reviewed. We begin with a brief discussion of Richardson's early work, which demonstrated the exact solvability of the pure pairing model, and then show how that work has evolved recently into a much richer class of exactly-solvable models. We then show how the Richardson solution leads naturally to an exact analogy between such quantum models and classical electrostatic problems in two dimensions. This is then used to demonstrate formally how BCS theory emerges as the large-N limit of the pure pairing Hamiltonian and is followed by several applications to problems of relevance to condensed matter physics, nuclear physics and the physics of confined systems. Some of the interesting effects that are discussed in the context of these exactly-solvable models include: (1) the crossover from superconductivity to a fluctuation-dominated regime in small metallic grains, (2) the role of the nucleon Pauli principle in suppressing the effects of high spin bosons in interacting boson models of nuclei, and (3) the possibility of fragmentation in confined boson systems. Interesting insight is also provided into the origin of the superconducting phase transition both in two-dimensional electronic systems and in atomic nuclei, based on the electrostatic image of the corresponding exactly-solvable quantum pairing models.