Strong Coupling Expansion for the Pairing Hamiltonian

Abstract

The paper is devoted to the effects of superconducting pairing in small metallic grains. It turns out that at strong superconducting coupling and in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem. We start with the strong coupling limit and develop a systematic expansion in powers of the inverse coupling constant for the many-particle spectrum of the system. The strong coupling expansion is based on the formal exact solution of the Richardson model and converges for realistic values of the coupling constant. We use this expansion to study the low energy excitations of the system, in particular energy and spin gaps in the many-body spectrum.

16 pages, 3 figures

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Cited by in corpus (36)

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• Exact mesoscopic correlation functions of the pairing model
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• Density-functional theory for the pairing Hamiltonian
• Analysis of the Strong Coupling Limit of the Richardson Hamiltonian using the Dyson Mapping
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• Arrays of Cooper Pair Boxes Coupled to a Superconducting Reservoir: `Superradiance' and `Revival.'
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• Superconducting charge qubits from a microscopic many-body perspective
• Yu-Shiba-Rusinov states, the BCS-BEC crossover, and the exact solution in the flat-band limit
• Nonlocality as the source of purely quantum dynamics of BCS superconductors
• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
• The multilevel pairing Hamiltonian versus the degenerate case
• The many levels pairing Hamiltonian for two pairs
• Subgap states in superconducting islands
• Perturbations on the superconducting state of metallic nanoparticles: influence of geometry and impurities
• Scaling properties of the pairing problem in the strong coupling limit