The fractal uncertainty principle and applications

Mardi 10 mars 11:00-12:00 - Nir Schwartz - LMO

Résumé : In 1927 Heisenberg has introduced a fundamental result in quantum mechanics — the uncertainty principle. Heisenberg’s result tells that a wave function cannot be localized simultaneously both in position and in momentum. We introduce a recent extension of the result due to Dyatlov and Bourgain adapted to the settings of « fractal » sets. We survey briefly their result and present several applications of it to problems in quantum chaos and to semi-classical analysis.

Lieu : Salle 3L8

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