Optimal-transport formulation of electronic density-functional theory
By Giuseppe M. Buttazzo, L. De Pascale, P. Gori-Giorgi. 2012
172 citations recorded by the source corpus.
SUMMARY The most challenging scenario for Kohn-Sham density functional theory, that is when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated here as an optimal transport (or mass transportation theory) problem, a well established field of mathematics and economics. In practice, we show that solving the problem of finding the minimum possible internal repulsion energy for $N$ electrons in a given density $\rho(\rv)$ is equivalent to find the optimal way of transporting $N-1$ times the density $\rho$ into itself, with cost function given by the Coulomb repulsion. We use this link to put the strong-interaction limit of density functional theory on firm grounds and to discuss the potential practical aspects of this reformulation.
Subfields: Atomic and Molecular Physics, and Optics, Catalysis, Inorganic Chemistry
View Paper: https://www.semanticscholar.org/paper/e17d538e2476b0110cdc3b841391df46e39cceae
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In Atomic and Molecular Physics, and Optics
In Catalysis
In Inorganic Chemistry
Citations in the corpus
- Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs (2015, background): “Seidl from the physical point of view and recalled in [3].”
- Multi-marginal optimal transport: theory and applications (2014, methodology): “The following theorem from [9, 21] is similar in spirit to Theorem 2.”
- Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters (2018, background): “and finance [5], condensed matter physics [8], and other applications [26].”