Grand Canonical Optimal Transport

par M. Luca Nenna (Université Paris Saclay)

lundi 25 oct. 2021, 11:00 → 12:00 Europe/Paris

1013 (Université de Paris - Bâtiment Sophie Germain)

In this talk I will firstly 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 a 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.