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The influence of an external electric field on the current in charged systems is investigated. The results beyond linear response from the classical hierarchy of density matrices are compared with the results from quantum kinetic theory. It is found that even an infinitesimal friction with the background changes the results in a noncontinuous way. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as the Debye-Onsager relaxation effect is obtained only if asymmetric screening is assumed. When considering the kinetic equation of one species, the other species have to be screened dynamically while the screening with the same species itself has to be performed statically. Other different approximations are discussed and compared.

Nonlinear relaxation field in charged systems under high electric fields