  Predictions are established for linear differential current-current
cross-correlations dSab/dV in a symmetrically biased three-terminal normal
metal-superconductor-normal metal (NSN) device. Highly transparent contacts
turn out to be especially interesting because they feature positive dSab/dV. At
high transparency, processes based on Crossed Andreev Reflection (CAR)
contribute only negligibly to the current and to dSab/dV. Under these
circumstances, current-current cross-correlations can be plausibly interpreted
as a coherent coupling between the two NS interfaces in the form of
synchronized Andreev and inverse Andreev reflections, corresponding to the
process where a pair of electron-like quasi-particles and a pair of hole-like
quasi-particles arrive from the normal electrodes and annihilate in the
superconductor. Hence, positive dSab/dV does not automatically imply CAR. For
tunnel contacts, dSab/dV is positive because of CAR. In between these two
extremities, at intermediate transparencies, dSab/dV is negative because both
processes which cause positive correlations, occur only with small amplitude.
We use scattering theory to obtain analytic expressions for current and noise,
and microscopic calculation using a tight binding model in order to obtain a
clear interpretation of the physical processes.
