BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function

Details BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function

2011-11-21

arxiv.org/abs/1111.4781v1

Physics

Condensed Matter

Superconductivity

11 pages, no figures

Scientific paper

A Bogoliubov approach to superconductivity shows that the wave function ansatz proposed by Bardeen, Cooper, Schrieffer just corresponds to the ground state of the Bogoliubov Hamiltonian, its energy being the extensive part of the BCS Hamiltonian energy. Extension to an arbitrary number of pairs in the energy layer where the potential acts, moreover shows that, although this wave function ansatz --- with all pairs condensed into the same state --- definitely differs from the exact wave function obtained by Richardson and Gaudin, it still provides the correct ground state energy for arbitrary pair number and potential strength, as obtained by analytically solving Richardson-Gaudin equations. This extension also reveals the existence of a super dilute and a super dense regime of pairs, with a gap different from the usual gap, these regimes being of importance to fully control the density-induced BEC-BCS cross-over.

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