Colloquium:: Exactly solvable Richardson-Gaudin models for manybody quantum systems
Colloquium:: Exactly solvable Richardson-Gaudin models for manybody quantum systems
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DOI：
10.1103/revmodphys.76.643
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发表时间：
2004-07-01
影响因子：
44.1
通讯作者：
Sierra, G
中科院分区：
文献类型：
--
作者：
Dukelsky, J;Pittel, S;Sierra, G
评述了精确可解Richardson-Gaudin模型在描述强对相关系统物理中的应用。本文首先简要讨论了Richardson的早期工作，该工作证明了纯配对模型的精确可解性，然后展示了该工作最近如何演变成更丰富的精确可解模型。理查德森解很自然地将这些量子模型与二维经典静电问题进行了精确的类比。然后用这个类比来正式证明BCS理论是如何成为纯配对哈密顿量的大n极限的。考虑了在与凝聚态物理、核物理和受限系统物理相关的问题中的几个应用。在这些精确可解模型的背景下讨论的一些有趣的效应包括(i)在小金属晶粒中从超导过渡到波动主导状态；（ii）核子泡利原理在抑制核子相互作用玻色子模型中高自旋玻色子效应中的作用，以及（iii）受限玻色子系统中碎裂的可能性。基于相应的精确可解量子配对模型的静电图像，对二维电子系统和原子核中超导相变的起源也提供了有趣的见解。
The use of exactly solvable Richardson-Gaudin models to describe the physics of systems with strong pair correlations is reviewed. The article begins with a brief discussion of Richardson's early work, which demonstrated the exact solvability of the pure pairing model, and then shows how that work has evolved recently into a much richer class of exactly solvable models. The Richardson solution leads naturally to an exact analogy between these quantum models and classical electrostatic problems in two dimensions. This analogy is then used to demonstrate formally how BCS theory emerges as the large-N limit of the pure pairing Hamiltonian. Several applications to problems of relevance to condensed-matter physics, nuclear physics, and the physics of confined systems are considered. Some of the interesting effects that are discussed in the context of these exactly solvable models include (i) the crossover from superconductivity to a fluctuation-dominated regime in small metallic grains; (ii) the role of the nucleon Pauli principle in suppressing the effects of high-spin bosons in interacting boson models of nuclei, and (iii) 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.