The elementary excitations of the BCS model in the canonical ensemble
G. Sierra, J. M. Roman (IFT, UAM/CSIC, Spain), J. Dukelsky (IEM,, CSIC, Spain)
TL;DR
This paper reviews the exact solutions for the ground state and elementary excitations of the BCS model in the canonical ensemble, highlighting the connection between Richardson and Gaudin equations in different coupling regimes.
Contribution
It clarifies the relationship between Richardson and Gaudin solutions, providing a classification of excitations in the BCS model.
Findings
Exact ground state and excitations summarized
Relationship between Richardson and Gaudin solutions established
Classification of excitations based on coupling strength
Abstract
We summarize previous works on the exact ground state and the elementary excitations of the exactly solvable BCS model in the canonical ensemble. The BCS model is solved by Richardson equations, and, in the large coupling limit, by Gaudin equations. The relationship between this two kinds of solutions are used to classiffy the excitations.
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