TY - CHAP
T1 - Quantum Optimal Transport
T2 - Quantum Couplings and Many-Body Problems
AU - Golse, François
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - This text is a set of lecture notes for a 4.5-hour course given at the Erdős 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 Golse et al. (Commun. Math. Phys. 343:165–205, 2016), and in Golse and Paul (Arch. Ration. Mech. Anal. 223:57–94, 2017). Lecture II discusses 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.
AB - This text is a set of lecture notes for a 4.5-hour course given at the Erdős 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 Golse et al. (Commun. Math. Phys. 343:165–205, 2016), and in Golse and Paul (Arch. Ration. Mech. Anal. 223:57–94, 2017). Lecture II discusses 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.
UR - https://www.scopus.com/pages/publications/85205120177
U2 - 10.1007/978-3-031-50466-2_3
DO - 10.1007/978-3-031-50466-2_3
M3 - Chapter
AN - SCOPUS:85205120177
T3 - Bolyai Society Mathematical Studies
SP - 91
EP - 202
BT - Bolyai Society Mathematical Studies
PB - Springer Science and Business Media Deutschland GmbH
ER -