Current-carrying ground states in mesoscopic and macroscopic systems.

I extend a theorem of Bloch, which concerns the net orbital current carried by an interacting electron system in equilibrium, to include mesoscopic effects. I obtain a rigorous upper bound to the allowed ground-state current in a ring or disk, for an interacting electron system in the presence of static but otherwise arbitrary electric and magnetic fields. I also investigate the effects of spin-orbit and current-current interactions on the upper bound. Current-current interactions, caused by the magnetic field produced at a point r by a moving electron at r8, are found to reduce the upper bound in a thin uniform ring by an amount that is determined by the self-inductance of the system. The upper bound is also compared with recent measurements of the persistent current in a single ring.