Vortex contribution to equilibrium currents

Like orbitals in atoms and molecules, persistent currents may appear in larger aggregates. Though classically, equilibrium magnetic moment of non-rotating objects is forbidden, it is known that equilibrium quantum circulating currents are allowed. Such currents were predicted to be periodic with the external magnetic field. It is shown that in general, whenever a periodic component is found, there must be a large aperiodic component forcing aperiodic contribution to the equilibrium magnetic moment as a function of the external field.