Optimal transport pseudometrics for quantum and classical densities

DOI10.1016/j.jfa.2022.109417zbMath1485.49053OpenAlexW4210651181MaRDI QIDQ2114126

François Golse, Thierry Paul

Publication date: 15 March 2022

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2022.109417

zbMATH Keywords

triangle inequalityoptimal transportKantorovich dualityquantum Wasserstein metric

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Duality theory (optimization) (49N15) Optimal transportation (49Q22)

Related Items (4)

Quantitative observability for the Schrödinger and Heisenberg equations: An optimal transport approach ⋮ A duality-based proof of the triangle inequality for the Wasserstein distances ⋮ Quantum Wasserstein isometries on the qubit state space ⋮ The Magnetic Liouville Equation as a Semiclassical Limit

Cites Work

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• On the mean field and classical limits of quantum mechanics
• An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy
• The Schrödinger equation in the mean-field and semiclassical regime
• Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality
• Coarse-scale representations and smoothed Wigner transforms
• Functional analysis, Sobolev spaces and partial differential equations
• On Wigner measures
• Remarks on the Monge-Kantorovich problem in the discrete setting
• Semiclassical evolution with low regularity
• Quantum optimal transport is cheaper
• Quantum optimal transport with quantum channels
• Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
• Exact equations for smoothed Wigner transforms and homogenization of wave propagation
• Foundation of quantum optimal transport and applications
• The Monge distance between quantum states
• Homogenization limits and Wigner transforms
• State Constraints in Convex Control Problems of Bolza

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