On the non-V-representability of currents in time-dependent many particle systems

TL;DR

This paper demonstrates that most time-dependent current densities in many-particle systems cannot be generated solely by scalar potentials, and interactions influence V-representability.

Contribution

It reveals the non-V-representability of arbitrary currents and how interactions affect this property in many-particle systems.

Findings

Most time-dependent currents are non-V-representable.

Interaction removal can change a current's V-representability.

Concrete example illustrating non-V-representability when interactions are turned off.

Abstract

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.