Lower semi-continuity of universal functional in paramagnetic current-density functional theory

TL;DR

This paper proves a fundamental mathematical property of current-density functional theory, ensuring the existence of minimizers and aligning its mathematical framework with standard density functional theory.

Contribution

It establishes the lower semi-continuity and expectation valuedness of the CDFT constrained-search functional, a key theoretical advancement.

Findings

Proves lower semi-continuity of the CDFT functional

Shows existence of minimizing density matrices in CDFT

Aligns CDFT mathematical framework with standard DFT

Abstract

A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semi-continuity and expectation valuedness of the CDFT constrained-search functional is proven, meaning that there is always a minimizing density matrix in the CDFT constrained-search universal density functional. These results place the mathematical framework of CDFT on the same footing as that of standard DFT.