MATS4400 Density Functional Theory for Strong Correlated Systems and Optimal Transport (5 cr)

Content

1st part: Ground state problem for Many-body Schödinger Equation; A brief introduction of Density Functional Theory: Hohenberg-Kohn functional, Kohm Sham Equations; Density Functional Theory for strongly correlated systems (adiabatic limit). Co-motion functions for spherically symmetric systems.

2nd part: Duality between the space of finite measures and continuous bounded functions; Monge and Monge-Kantorovich problems, existence of optimal plans, Kantorovich duality and existence of Kantorovich potentials. Monge problem (two marginal case) and Wasserstein distances. Multi-marginal Optimal Transport for the attractive harmonic case (existence of Monge minimizers). Study the two electrons (marginals) case for Coulomb costs and the N electrons (multi-marginal) case for radially symmetric densities.

Depending of the interests of the students the following topics (not limited of) can be covered as well: Regularity of Kantorovich potentials for Coulomb costs. Entropic Transport. Optimal Transport for Repulsive harmonic costs. Semi-classical limit of the Hohenberg-Kohn functional.

Completion methods

Homework assignments and a course exam. Grades will be based on the homeworks (1/3) and the final exam (2/3).

Assessment details

Homework assignments and a course exam. Grades will be based on the homeworks (1/3) and the final exam (2/3).