  The electromagnetic response of hot QCD matter to decaying external magnetic
fields is investigated. We examine the validity of Ohm's law and find that the
induced electric current increases from zero and relaxes towards the value from
Ohm's law. The relaxation time is larger than the lifetime of the external
magnetic field for the QCD matter in relativistic heavy-ion collisions. The
lower than expected electric current significantly suppresses the induced
magnetic field and makes the electromagnetic response incomplete. We
demonstrate the incomplete electromagnetic response of hot QCD matter by
calculations employing the parton transport model combined with the solution of
Maxwell's equations. Our results show a strong suppression by two orders of
magnitude in the magnetic field, relatively to calculations assuming the
validity of Ohm's law. This may undermine experimental efforts to measure
magnetic-field-related effects in heavy-ion collisions.
