Quantum Optimal Transport: Quantum Couplings and Many-Body Problems
Résumé
This text is a set of lecture notes for a 4.5-hour course given at the Erd\H os Center (Rényi Institute, Budapest) during the Summer School ``Optimal Transport on Quantum Structures'' (September 19th-23rd, 2023). Lecture I introduces the quantum analogue of the Wasserstein distance of exponent 2 defined in [F. Golse, C. Mouhot, T. Paul: Comm. Math. Phys. 343 (2016), 165-205], and in [F. Golse, T. Paul: Arch. Ration. Mech. Anal. 223 (2017) 57-94]. Lecture II presents various applications of this quantum analogue of the Wasserstein distance of exponent 2, while Lecture III discusses several of its most important properties, such as the triangle inequality, and the Kantorovich duality in the quantum setting, together with some of their implications.
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FGolseQOTPest.pdf (7.43 Mo)
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Concave.pdf (45.07 Ko)
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GC.pdf (26.04 Ko)
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QDist4.pdf (237.93 Ko)
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WavePacket.pdf (5.94 Mo)
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WavePacket2.pdf (62.34 Ko)
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