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Theoretical and Mathematical Physics

Generalization of the Bardeen-Cooper-Schrieffer method for pair interactions

Геннадий Васильевич Коваль, Виктор Павлович Маслов

Published Mar 1, 2008• 3 citations
Publisher
DOI
10.1007/s11232-008-0040-9

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Bardeen–Cooper–Schrieffer (BCS)-like models for permutation invariant electronic interactions are investigated in terms of recent rigorous mean-field methods. Their limiting dynamics is constructed in the Heisenberg picture on (extensions of) the full canonical commutation relation (CAR) algebra and also restricted to (extensions of) the pair algebra. The classical part of the proper BCS dynamics on the CAR algebra is shown to exhibit 15 macroscopic collective variables, the time dependence of which is explicitly integrated and discussed.
Abstract One of the important steps leading to the successful formulation of the microscopic theory of superconductivity was the model calculation performed by Cooper (1956) which showed that two electrons, interacting above a filled Fermi sea, had a bound state in the presence of an arbitrarily weak attractive interaction. This chapter first examines Cooper’s calculation. The success of the Cooper model calculation in producing a bound state, with its implication that a proper many-body theory would contain a gap in the excitation spectrum, strongly suggests that the ground state wave function should be constructed from pairs of electrons. However, it is difficult to perform calculations using the many-body pair wave function from Cooper’s model. The chapter then introduces the wave function proposed by Bardeen, Cooper, and Schrieffer (BCS) as an alternative.