  We study the temporal response of the electric current in an electrolyte
under a sudden switch on or switch off of an external electric field of
arbitrary magnitude. We use Stochastic Density Functional Theory including
hydrodynamic interactions to express the current as a function of the ionic
correlations. Assuming small density fluctuations, we linearize the field
theory to compute the correlations in the transient regime. We first show that
the correlations do not follow the same trajectory when the field is switched
on or switched off. Accordingly, the behavior of the current differs in the two
cases: it decays exponentially when the field is switched off, but it relaxes
algebraically to its stationnary value when the field is switched on. This
difference is a non-linear effect since an exponential relaxation is recovered
in both cases in the weak field limit.
