64 research outputs found
Kohn-Sham computation and the bivariate view of density functional theory
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.Comment: supersedes arXiv:1807.0612
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