Mean-field limit and semiclassical approximation for quantum particle systems
Year: 2009
Type: article
Abstract: Introduction 1. Classical Mean-Field limit 1.1 Setting of the problem: general features and known results 1.2 The Vlasov equation 1.3 The Vlasov dynamics as the continuum limit of the N -particle MeanField dynamics 1.4 Hierarchies and Propagation of Chaos 2. Quantum Mean-Field limit 2.1 Setting of the problem: general features and known results 2.1.1 The density matrix formalism 2.1.2 The limit N → ∞ 2.2 Quantum BBGKY hierarchy and its formal limit as N → ∞ 2.3 Mean-Field limit for bounded potentials 2.3.1 An alternative approach 2.3.2 Mean-Field limit for the Coulomb potential 3. Mean-Field limit VS Semiclassical approximation 3.1 The Wigner formulation 3.2 The Mean-lield system in the Wigner formalism 3.2.1 The Wigner BBGKY hierarchy 3.3 The Hartree dynamics in the Wigner formalism 3.4 The limit N → ∞ 3.5 Alternative approaches
Author: Federica Pezzotti
Institution: University of the Basque Country
Language: Italian
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2403419159