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Nonlinear relaxation field in charged systems under high electric fields

The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. 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 Debye - Onsager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared.