Spin current shot noise as a probe of interactions in mesoscopic systems

It is shown that the spin resolved current shot noise can probe attractive or repulsive interactions in mesoscopic systems. This is illustrated in two physical situations : i) a normal-superconducting junction where the spin current noise is found to be zero, and ii) a single electron transistor (SET), where the spin current noise is found to be Poissonian. Repulsive interactions may also lead to weak attractive correlations (bunching of opposite spins) in conditions far from equilibrium. Spin current shot noise can be used to measure the spin relaxation time $T_1$, and a set-up is proposed in a quantum dot geometry.