Séminaire Analyse Numérique et EDP
Grand Canonical Optimal Transport
06
Oct. 2022
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.