The non-linear adiabatic response of some simple quantum systems to weak but finite driving forces is investigated. In particular, the effect of the electric field on the motion of a charged particle in a weak periodic potential, in a narrow one-dimensional energy band, and in a two-level system, is calculated. The possibility of the linear high field response is demonstrated. Such a macroscopic linear response is different from the microscopic Green-Kubo response because of the non-linear dynamic behaviour of systems. Kinetic coefficients and susceptibilities for realistic systems may be complicated functions of driving forces even if the external perturbations are weak. Different quasi-linear regions of response are possible.
