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Open PDE & Analysis Seminar and Lectures

Dr Thierry Paul (CNRS & LJLL Sorbonne Universités)

Optimal transport and quantum mechanics: more facts and applications

11th June 2021, 4pm (Paris time)

Abstract : After showing that the extension of the Monge-Kantorovich-Wasserstein distance introduced in the talk by F. Golse is more convenient to separate density matrices than the usual Schatten topologies usually used in quantum mechanics, we shall show how (and explain why) they produce a cost for the quantum bipartite matching problem which is cheapper than the corresponding classical one. We shall then show that a quantum version of the Kantorovich duality provides a form of Knott-Smith-Brenier theorem in quantum mechanics, under technical conditions on the density matrices involved, with a suitable quantum definition of the gradient of an observable, naturally constructed on the classical one. The finite rank case, always tractable, will give rise itself to a non-gradient «flow » without classical counterpart. Finally, we will study transport associated to a semiquantum analogue of the Wasserstein distances and show that they involve a generalization the Legendre transform between classical and quantum densities. (Based on a series of works with E. Caglioti, F. Golse and C. Mouhot)



Zoom link

This is the link to this talk:

https://univ-cotedazur.zoom.us/j/6040812151
Meeting ID: 604 081 2151.
Acces code: (None).





Organisers

Thomas Alazard (ENS Paris-Saclay)     Nicolas Burq (Orsay)     Clément Mouhot (Cambridge)
Iván Moyano (Nice)     Benoit Pausader (Brown)     Marjolaine Puel (Cergy-Pontoise)