Strong semiclassical approximation of Wigner functions for the Hartree dynamics

DOI10.4171/RLM/613zbMath1235.81100arXiv1009.0470MaRDI QIDQ661148

Mario Pulvirenti, Federica Pezzotti, Thierry Paul, Agissilaos G. Athanassoulis

Publication date: 19 February 2012

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.0470

zbMATH Keywords

semiclassical analysisWigner formalismHartree dynamicsHusimi transform

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) 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)

Related Items (23)

Effective dynamics of interacting fermions from semiclassical theory to the random phase approximation ⋮ From the Hartree dynamics to the Vlasov equation ⋮ A new method and a new scaling for deriving fermionic mean-field dynamics ⋮ Mean field evolution of fermions with Coulomb interaction ⋮ Propagation of Moments for Large Data and Semiclassical Limit to the Relativistic Vlasov Equation ⋮ Effective dynamics of extended Fermi gases in the high-density regime ⋮ Strong semiclassical limits from Hartree and Hartree-Fock to Vlasov-Poisson equations ⋮ A mixed-norm estimate of the two-particle reduced density matrix of many-body Schrödinger dynamics for deriving the Vlasov equation ⋮ The Magnetic Liouville Equation as a Semiclassical Limit ⋮ On the \(L^2\) rate of convergence in the limit from the Hartree to the Vlasov-Poisson equation ⋮ Mean-field evolution of fermionic systems ⋮ From the Hartree Equation to the Vlasov--Poisson System: Strong Convergence for a Class of Mixed States ⋮ Semiclassical propagation of coherent states for the Hartree equation ⋮ Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations ⋮ Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data ⋮ The Schrödinger equation in the mean-field and semiclassical regime ⋮ From Hartree dynamics to the relativistic Vlasov equation ⋮ Semiclassical limit to the Vlasov equation with inverse power law potentials ⋮ Hartree corrections in a mean-field limit for fermions with Coulomb interaction ⋮ Empirical measures and quantum mechanics: applications to the mean-field limit ⋮ Mean field dynamics of interacting fermionic systems ⋮ Propagation of moments and semiclassical limit from Hartree to Vlasov equation ⋮ Convergence towards the Vlasov-Poisson equation from the \(N\)-fermionic Schrödinger equation

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