Non-equilibrium excess noise of a short quasi one-dimensional constriction
between two superconductors is considered. A general expression for the
current-current correlation function valid for arbitrary temperatures and bias
voltages is derived. This formalism is applied to a current-carrying quantum
channel with perfect transparency. Contrary to a transparent channel separating
two normal conductors, a weak link between two superconductors exhibits a
finite level of noise. The source of noise is fractional Andreev scattering of
quasiparticles with energies ∣E∣ greater than the half-width Δ of the
superconducting gap. For high bias voltages, V≫Δ/e, the relation
between the zero-frequency limit of the noise spectrum, S(0), and the excess
current Iexc reads S(0)=(1/5)∣e∣Iexc. As Δ→0 both the excess noise and the excess current vanish linearly in
Δ, %∝Δ, their ratio being constant.Comment: 8 pages (Latex), 1 figur