Prohibition of equilibrium spin currents in multiterminal ballistic devices

It is shown that in the multiterminal ballistic devices with intrinsic spin-orbit interaction connected to normal metal contacts there are no equilibrium spin currents present at any given electron energy. Evidently, this statement holds also after the integration over all occupied states. Based on this observation, several scenarios involving nonequilibrium spin currents are identified and further analyzed. In particular, it is shown that an arbitrary single-channel two-terminal device cannot polarize transient currents. The same is true for the single-channel output terminal of an N-terminal device when all N-1 inputs are connected in parallel.