The non-uniform electron gas

TL;DR

This paper rigorously defines and analyzes the properties of non-uniform electron gases using advanced density functional theory frameworks, focusing on systems with lattice-periodic background densities.

Contribution

It introduces a rigorous definition of non-uniform electron gases via Levy-Lieb functionals and establishes their thermodynamic limits, extending theoretical understanding.

Findings

Defined quantum and classical non-uniform electron gases rigorously.

Established thermodynamic limits for these systems.

Analyzed properties based on lattice-periodic background densities.

Abstract

The non-uniform (or inhomogeneous) electron gas has received much attention in many-body quantum mechanics and quantum chemistry in the early days of density functional theory, mainly as a theoretical device to construct gradient approximations via linear response theory. In this article, motivated by the recent works of Lewin, Lieb and Seiringer, we propose a definition of the quantum (resp. classical) non-uniform electron gas through the use of the grand-canonical Levy-Lieb functional (resp. the grand-canonical strictly correlated electrons functional), establish these systems as rigorous thermodynamic limits and analyze their basic properties. The non-uniformity of the gas comes from an arbitrary lattice-periodic background density.