Electron kinetics in isolated mesoscopic rings driven out of equilibrium
  Kinetic theory of nonlinear current response to an external field is developed for mesoscopic normal metal rings threaded by a magnetic flux. General expressions for direct current (DC) are derived for a non-equilibrium regime. These expressions describe simultaneously a contribution to DC made by a non-equilibrium (external) field, as well as the contribution caused by interaction with intrinsic fields. Contributions of electron-electron and electron-phonon interactions to the direct current in a non-equilibrium systems are studied. The kinetic equation for electrons in a disordered metal ring is solved with taking into account the Coulomb and electron-phonon interactions. This gives an estimate of an overheating of the pumped electron system. 
V.I.Yudson and V.E.Kravtsov