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SUMMARY:Thierry Paul (CNRS & Ecole Polytechnique)
DTSTART:20210611T140000Z
DTEND:20210611T150000Z
DTSTAMP:20260423T021045Z
UID:OpenPDEA/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OpenPDEA/9/"
 >(Seminar) Optimal transport and quantum mechanics: more facts and applica
 tions</a>\nby Thierry Paul (CNRS & Ecole Polytechnique) as part of Open PD
 E and analysis seminar and lectures\n\n\nAbstract\nAfter 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 sho
 w how (and explain why) they produce a cost for the quantum bipartite matc
 hing problem which is cheapper than the corresponding classical one. We sh
 all then show that a quantum version of the Kantorovich duality provides a
  form of Knott-Smith-Brenier theorem in quantum mechanics\, under technica
 l conditions on the density matrices involved\, with a suitable quantum de
 finition of the gradient of an observable\, naturally constructed on the c
 lassical one. The finite rank case\, always tractable\, will give rise its
 elf to a non-gradient «flow » without classical counterpart. Finally\, w
 e will study transport associated to a semiquantum analogue of the Wassers
 tein distances and show that they involve a generalization the Legendre tr
 ansform between classical and quantum densities. (Based on a series of wor
 ks with E. Caglioti\, F. Golse and C. Mouhot)\n
LOCATION:https://researchseminars.org/talk/OpenPDEA/9/
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