Séminaire Analyse Numérique et EDP
Grand Canonical Optimal Transport
oct. 2022
Intervenant : Luca Nenna
Institution : LMO - Paris Saclay
Heure : 14h00 - 15h00
Lieu : Salle 3L8

In this talk I will briefly review standard Multi-Marginal Optimal Transport (a number N of marginals is fixed) focusing, in particular, on the applications in Quantum Mechanics (in this case the marginals are all the same and represent the electron density). I will then extend the Optimal Transportation problem to the grand canonical setting: only the expected number of marginals/electrons is now given (i.e. we can now define an OT problem with a fractional number of marginals). I will compare these two problems and show how they behave differently despite considering the same cost functions. Existence of minimisers, Monge solution, duality, entropic formulation and numerics will be discussed.

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