André Laestadius: Non-existence of a Hohenberg-Kohn Variational Principle in Total Current Density Functional Theory

Abstract. In a joint work with Prof. M. Benedicks the non-existence of a Hohenberg-Kohn variational principle for current density functional theory has been established. For a many-electron system, whether the particle density and the total current density are sufficient to determine the one-body potential and the vector potential, is still an open question. In this recent work, we have shown that the generalized Hohenberg-Kohn energy functional can be minimal for densities that are not the ground-state densities. Furthermore, for an arbitrary number of electrons and under the assumption that a Hohenberg-Kohn theorem exists formulated with the particle density and the total current density, we have shown that a variational principle for Total Current Density Functional Theory as that of Hohenberg-Kohn for Density Functional Theory does not exist.