Coherence Factors Beyond the BCS Expressions -- A Derivation

Abstract

We present a derivation of a previously announced result for matrix elements between exact eigenstates of the pairing Hamiltnonian. Our results, which generalize the well known BCS (Bardeen-Cooper-Schrieffer) expressions for what is known as 'coherence factors', are derived based on the Slavnov formula for overlaps between Bethe-ansatz states, thus making use of the known connection between the exact diagonalization of the BCS Hamiltonian, due to Richardson, and the algebraic Bethe ansatz. The resulting formula has a compact form after a suitable parameterization of the Energy plane. Although we apply our method here to the pairing Hamiltonian, it may be adjusted to study what is termed the 'Sutherland limit' for exactly solvable models, namely where a macroscopic number of rapidities form a large string.

References in corpus (5)

• Classical Limit of the Three-Point Function from Integrability
• Exact expectation values within Richardson's approach for the pairing Hamiltonian in a macroscopic system
• Electron-hole symmetry and solutions of Richardson pairing model
• Coherence Factors Beyond the BCS Result
• Multi-condensate states in BCS superconductors

Cited by in corpus (4)

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• Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model