We argue that an arbitrarily chosen time-dependent current density is generically non-$V$-representable 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.

• Received 7 January 2005

DOI:https://doi.org/10.1103/PhysRevB.71.245103