Density functional theory for collisionless plasmas -- equivalence of fluid and kinetic approaches

TL;DR

This paper demonstrates that classical collisionless plasmas can be equivalently described by fluid equations derived from density functional theory, bridging the gap between kinetic and fluid models.

Contribution

It establishes a theoretical equivalence between the Vlasov kinetic description and fluid equations for collisionless plasmas using time-dependent DFT.

Findings

Exact closure relations for plasma dynamics exist within DFT.

Fluid and kinetic descriptions are fundamentally compatible.

DFT guarantees a full representation of Vlasov dynamics.

Abstract

Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed matter physics, atomic physics, and quantum chemistry. DFT establishes that a system of $N$ interacting electrons can be described uniquely by its single-particle density $n(\boldsymbol{r})$, instead of the $N$-body wave function, yielding an enormous gain in terms of computational speed and memory storage space. Here, we use time-dependent DFT to show that a classical collisionless plasma can always, in principle, be described by a set of fluid equations for the single-particle density and current. The results of DFT guarantee that an exact closure relation, fully reproducing the Vlasov dynamics, necessarily exists, although it may be complicated (nonlocal in space and time, for instance) and difficult to obtain in practice. This goes against the common wisdom in plasma physics that the Vlasov and fluid descriptions are mutually incompatible, with the latter inevitably missing some "purely kinetic" effects.