  The dynamics of BCS (Bardeen-Cooper-Schrieffer) superconductors is fairly
well understood due to the availability of a mean field solution for the
pairing Hamiltonian, a solution which gives the quantum state of superconductor
as a state of almost-free fermions interacting only with a condensate. As a
result, transition probabilities may be computed, and expressed in terms of
matrix elements of electron creation and annihilation operators between
approximate eigenstates. These matrix elements are also called 'coherent
factors'. Mean-field theory is however not sufficient to describe all
eigenstates of a superconductor, a deficiency which is hardly important in (or
very close) to equilibrium, but one that becomes relevant in certain out of
equilibrium situations. We report here on a computation of matrix elements
(coherence factors) for the pairing Hamiltonian between any 'two-arc'
eigenstates in the thermodynamic limit.
