Abstract

The natural degrees of freedom associated with pairing correlations are incorporated in a generalized BCS ansatz to describe ultrasmall superconducting grains. Pairing fluctuations associated with finite systems are fully taken into account. As an example, the formalism is applied to the reduced pairing Hamiltonian where we reproduce the exact solutions in the weak, crossover, and strong pairing regimes. The physical insight of the ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in more complex and realistic systems than the one discussed here.

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