Finite Size Corrections for the Pairing Hamiltonian

Abstract

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies.

22 pages, 1 figure

References in corpus (7)

• Gate-Voltage Studies of Discrete Electronic States in Al Nanoparticles
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• Integrability of the pairing hamiltonian
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Cited by in corpus (36)

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• Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
• Dynamical correlation functions of the mesoscopic pairing model
• Migdal-Eliashberg theory as a classical spin chain
• Possibility of Electron Pairing in Small Metallic Nanoparticles
• Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids
• Effect of a Zeeman field on the superconductor-ferromagnet transition in metallic grains
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• From one to $N$ Cooper pairs, step by step
• Shape resonances and shell effects in thin-film multiband superconductors
• Combined effect of thermal and quantum fluctuations in superconducting nanostructures: a path integral approach
• Pairing Correlations in Finite Systems: From the weak to the strong fluctuations regime
• Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime
• Density-functional theory for the pairing Hamiltonian
• Real and imaginary energy gaps: a comparison between single excitation Superradiance and Superconductivity and robustness to disorder
• Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian
• Exact solution for the inhomogeneous Dicke model in the canonical ensemble: thermodynamical limit and finite-size corrections
• Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations
• Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models
• Mesoscopic pairing without superconductivity
• Electron-hole symmetry and solutions of Richardson pairing model
• Gaussian ensemble for quantum integrable dynamics
• Applicability of Bardeen-Cooper-Schrieffer theory to small-sized superconductors: role of Cooper-pair binding energy
• Fermi Surface Volume of Interacting Systems
• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
• Nonlocality as the source of purely quantum dynamics of BCS superconductors
• Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological $p$-wave superfluid
• Superconducting fluctuations in small grains - the Universal Hamiltonian and the reduced BCS model
• Trotter transition in BCS pairing dynamics
• Scaling properties of the pairing problem in the strong coupling limit