  We argue that an arbitrarily chosen time-dependent current density is
generically non-Vrepresentable in a many-particle system, i.e., it cannot be
obtained by applying only a time dependent scalar potential to the system.
Furthermore we show by a concrete example that even a current that is
V-representable in an interacting many-particle system may (and in general
will) turn out to be non-V-representable when the interaction between the
particles is turned off.
