Buttazzo, Giuseppe and Pascale, Luigi De and Gori-Giorgi, Paola (2012) *Optimal-transport formulation of electronic density-functional theory.* Physical review. A, Atomic, Molecular, and Optical Physics, 85 . 062502. ISSN 1094-1622

## Abstract

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.

Item Type: | Article |
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Additional Information: | Imported from arXiv |

Subjects: | Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |

Divisions: | Dipartimenti (from 2013) > DIPARTIMENTO DI MATEMATICA |

Depositing User: | dott.ssa Sandra Faita |

Date Deposited: | 05 Aug 2013 12:48 |

Last Modified: | 05 Aug 2013 12:48 |

URI: | http://eprints.adm.unipi.it/id/eprint/1342 |

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