Integrable models for confined fermions: applications to metallic grains

Abstract

We study integrable models for electrons in metals when the single particle spectrum is discrete. The electron-electron interactions are BCS-like pairing, Coulomb repulsion, and spin exchange coupling. These couplings are, in general, nonuniform in the sense that they depend on the levels occupied by the interacting electrons. By using the realization of spin 1/2-operators in terms of electrons the models describe spin 1/2 models with nonuniform long range interactions and external magnetic field. The integrability and the exact solution arise since the model Hamiltonians can be constructed in terms of Gaudin models. Uniform pairing and the resulting orthodox model correspond to an isotropic limit of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.

elsart, 21 pages, 4 eps figures. Version emended from few misprints

References in corpus (4)

• The Statistical Theory of Quantum Dots
• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Integrable model for interacting electrons in metallic grains
• Thermodynamic properties of a small superconducting grain

Cited by in corpus (21)

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• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
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