Non- V -representability of currents in time-dependent many-particle systems

Abstract

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.