Density functional theory on phase space

Abstract

Forty-five years after the point de départ [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the electron density still eludes us -- and possibly will do so forever [2]. In what follows we examine a formulation in the same spirit with phase space variables. The validity of Hohenberg-Kohn-Levy-type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase-space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation-exchange functionals on phase space. A new proof of the overbinding property of the Mueller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the Thomas-Fermi model.

Latex, 48 pages, 1 figure; v2: minor changes, references added. v3: minor update to coincide with published version

References in corpus (8)

• The Pauli principle revisited
• Mueller's Exchange-Correlation Energy in Density-Matrix-Functional Theory
• Leading corrections to local approximations
• The Pauli exclusion principle and beyond
• Density functional theory on phase space
• Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem
• Das asymptotische Verhalten der Grundzustandsenergie des Muellerfunktionals fuer schwere Atome
• Exact phase space functional for two-body systems

Cited by in corpus (9)

• Entanglement in N-harmonium: bosons and fermions
• Density functional theory on phase space
• The lowest excited configuration of harmonium
• Notes on "quantum gravity" and non-commutative geometry
• Testing one-body density functionals on a solvable model
• Static correlated functionals for reduced density matrix functional theory
• Physical Wigner functions
• Orbital-Free Quasi-Density Functional Theory
• Exact phase space functional for two-body systems