  We perform the first systematic study of the nonlinear electromagnetic
currents induced by external electromagnetic field in quark-gluon plasma, both
in the two cases that the inhomogeneity of electromagnetic field is small
(large) so that the collision effect is important (negligible). In the former
case, we list and classify possible components of the currents in a systematic
way, and make an order estimate of each component by using the Boltzmann
equation in the relaxation time approximation. In the latter case, we
explicitly calculate the quadratic current by using the Vlasov equation, and
find that the current generated by the chiral magnetic effect and the quadratic
current can have the same order of magnitude by using the Kadanoff-Baym
equation. We also demonstrate this property by using a possible configuration
of electromagnetic field realized in heavy ion collision.
