Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime

Abstract

We review the exact treatment of the pairing correlation functions in the canonical ensemble. The key for the calculations has been provided by relating the discrete BCS model to known integrable theories corresponding to the so called Gaudin magnets with suitable boundary terms. In the present case the correlation functions can be accessed beyond the formal level, allowing the description of the cross-over from few electrons to the thermodynamic limit. In particular, we summarize the results on the finite size scaling behavior of the canonical pairing clarifying some puzzles emerged in the past. Some recent developments and applications are outlined.

11 pages, 7 figures, revtex4

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• Quantum phase transitions in the interacting boson model
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Cited by in corpus (8)

• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Spin decoherence due to a randomly fluctuating spin bath
• Inner products in integrable Richardson-Gaudin models
• Trigonometric sl(2) Gaudin model with boundary terms
• Integrability of an extended d+id-wave pairing Hamiltonian
• A variational method for integrability-breaking Richardson-Gaudin models
• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
• Jordanian deformation of the open sl(2) Gaudin model