2023/05/28 by Paul E. Lammert, Lammert, Paul E.
Chemistry · Physics and Astronomy · #FOS: Physical sciences #History and advancements in chemistry #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2305.17795
openalex publication_date 2023/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Informed by an abstraction of Kohn-Sham computation called a KS machine, a functional analytic perspective is developed on mathematical aspects of density functional theory. A natural semantics for the machine is bivariate, consisting of a sequence of potentials paired with a ground density. Although the question of when the KS machine can converge to a solution (where the potential component matches a designated target) is not resolved here, a number of related ones are. For instance: Can the machine progress toward a solution? Barring presumably exceptional circumstances, yes in an energetic sense, but using a potential-mixing scheme rather than the usual density-mixing variety. Are energetic and function space distance notions of proximity-to-solution commensurate? Yes, to a significant degree. If the potential components of a sequence of ground pairs converges to a target density, do the density components cluster on ground densities thereof? Yes, barring particle number drifting to infinity.