Aharonov-Bohm magnetization of mesoscopic rings caused by inelastic relaxation

The magnetization of a system of many mesoscopic rings under nonequilibrium conditions is considered. The corresponding disorder-averaged current in a ring I(phi) is shown to be a sum of the thermodynamic and kinetic contributions both resulting from the electron-electron interaction. The thermodynamic part can be expressed through the diagonal matrix elements J(mumu) of the current operator in the basis of exact many-body eigenstates and is a generalization of the equilibrium persistent current. The novel kinetic part is present only out of equilibrium and is governed by the off-diagonal matrix elements J(munu). It has drastically different temperature and magnetic field behavior.