Empirical measures and quantum mechanics: applications to the mean-field limit

DOI10.1007/s00220-019-03357-zzbMath1417.81127arXiv1711.08350OpenAlexW2769428211WikidataQ128306831 ScholiaQ128306831MaRDI QIDQ2311919

François Golse, Thierry Paul

Publication date: 4 July 2019

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08350

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Many-body theory; quantum Hall effect (81V70) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) (n)-body problems (70F10) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (12)

A new perspective on Wasserstein distances for kinetic problems ⋮ The Random Batch Method for N-Body Quantum Dynamics ⋮ Quantum mean-field games ⋮ Propagation of Moments for Large Data and Semiclassical Limit to the Relativistic Vlasov Equation ⋮ On quantum Sobolev inequalities ⋮ Strong semiclassical limits from Hartree and Hartree-Fock to Vlasov-Poisson equations ⋮ From the Hartree Equation to the Vlasov--Poisson System: Strong Convergence for a Class of Mixed States ⋮ Combined mean-field and semiclassical limits of large fermionic systems ⋮ Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data ⋮ The magnetized Vlasov-Ampère system and the Bernstein-Landau paradox ⋮ Semiclassical limit to the Vlasov equation with inverse power law potentials ⋮ The law of large numbers for quantum stochastic filtering and control of many-particle systems

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