TY - JOUR

T1 - Coherence factors beyond the BCS expressions - A derivation

AU - Gorohovsky, G.

AU - Bettelheim, E.

PY - 2014/1/17

Y1 - 2014/1/17

N2 - We present a derivation of a previously announced result for matrix elements between exact eigenstates of the pairing Hamiltonian. Our results, which generalize the well-known Bardeen-Cooper-Schrieffer (BCS) (Bardeen et al 1957 Phys. Rev. 108 1175; 1957 Phys. Rev. 106 162) expressions for what are known as 'coherence factors', are derived based on the Slavnov (1989 Theor. Math. Phys. 79 502) 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 (1963 Phys. Lett. 3 277; 1964 Nucl. Phys. A 52 221), 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' (Sutherland 1995 Phys. Rev. Lett. 74 816) for exactly solvable models, namely where a macroscopic number of rapidities form a large string.

AB - We present a derivation of a previously announced result for matrix elements between exact eigenstates of the pairing Hamiltonian. Our results, which generalize the well-known Bardeen-Cooper-Schrieffer (BCS) (Bardeen et al 1957 Phys. Rev. 108 1175; 1957 Phys. Rev. 106 162) expressions for what are known as 'coherence factors', are derived based on the Slavnov (1989 Theor. Math. Phys. 79 502) 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 (1963 Phys. Lett. 3 277; 1964 Nucl. Phys. A 52 221), 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' (Sutherland 1995 Phys. Rev. Lett. 74 816) for exactly solvable models, namely where a macroscopic number of rapidities form a large string.

UR - http://www.scopus.com/inward/record.url?scp=84891352497&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/2/025001

DO - 10.1088/1751-8113/47/2/025001

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AN - SCOPUS:84891352497

SN - 1751-8113

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 2

M1 - 025001

ER -