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arXiv · 1011.3691

The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

Stijn De Baerdemacker
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Abstract

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.

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Stijn De Baerdemacker. 2010-11-16. The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing. https://doi.org/10.1088/1742-6596%2F284%2F1%2F012020

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