  We investigate time-adaptive Magnus-type integrators for the numerical
approximation of a Mott transistor. The rapidly attenuating electromagnetic
field calls for adaptive choice of the time steps. As a basis for step
selection, asymptotically correct defect-based estimators of the local error
are employed. We analyze the error of the numerical approximation in the
presence of the unsmooth external potential and demonstrate the advantages of
the adaptive approach.
