dorsal/arxiv
View SchemaExactly solvable Richardson-Gaudin models for many-body quantum systems
| Authors | J. Dukelsky, S. Pittel, G. Sierra |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0405011 |
| URL | https://arxiv.org/abs/nucl-th/0405011 |
| DOI | 10.1103/RevModPhys.76.643 |
| Journal | Rev.Mod.Phys.76:643-662,2004 |
Abstract
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.
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"abstract": "The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the\nphysics of systems with strong pair correlations is reviewed. We begin with a\nbrief discussion of Richardson\u0027s early work, which demonstrated the exact\nsolvability of the pure pairing model, and then show how that work has evolved\nrecently into a much richer class of exactly-solvable models. We then show how\nthe Richardson solution leads naturally to an exact analogy between such\nquantum models and classical electrostatic problems in two dimensions. This is\nthen used to demonstrate formally how BCS theory emerges as the large-N limit\nof the pure pairing Hamiltonian and is followed by several applications to\nproblems of relevance to condensed matter physics, nuclear physics and the\nphysics of confined systems. Some of the interesting effects that are discussed\nin the context of these exactly-solvable models include: (1) the crossover from\nsuperconductivity to a fluctuation-dominated regime in small metallic grains,\n(2) the role of the nucleon Pauli principle in suppressing the effects of high\nspin bosons in interacting boson models of nuclei, and (3) the possibility of\nfragmentation in confined boson systems. Interesting insight is also provided\ninto the origin of the superconducting phase transition both in two-dimensional\nelectronic systems and in atomic nuclei, based on the electrostatic image of\nthe corresponding exactly-solvable quantum pairing models.",
"arxiv_id": "nucl-th/0405011",
"authors": [
"J. Dukelsky",
"S. Pittel",
"G. Sierra"
],
"categories": [
"nucl-th",
"cond-mat.supr-con",
"nlin.SI",
"quant-ph"
],
"doi": "10.1103/RevModPhys.76.643",
"journal_ref": "Rev.Mod.Phys.76:643-662,2004",
"title": "Exactly solvable Richardson-Gaudin models for many-body quantum systems",
"url": "https://arxiv.org/abs/nucl-th/0405011"
},
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