Mesoscopic effects in superconductor-ferromagnet-superconductor junctions

We show that at zero temperature the supercurrent through the superconductor

• ferromagnetic metal - superconductor junctions does not decay exponentially with the thickness $L$ of the junction. At large $L$ it has a random sample-specific sign which can change with a change in temperature. In the case of mesoscopic junctions the phase of the order parameter in the ground state is a random sample-specific quantity. In the case of junctions of large area the ground state phase difference is $\pm \pi \mathrm{/}2$.