Wigner measures approach to the classical limit of the Nelson model: convergence of dynamics and ground state energy

DOI10.1007/s10955-014-1079-7zbMath1302.82009arXiv1403.2327OpenAlexW3103560789MaRDI QIDQ478441

Marco Falconi, Zied Ammari

Publication date: 3 December 2014

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.2327

zbMATH Keywords

ground state energyclassical limitWigner measuresNelson modelKlein-Gordon-Schrödinger equation

Mathematics Subject Classification ID

Model quantum field theories (81T10) KdV equations (Korteweg-de Vries equations) (35Q53) Classical equilibrium statistical mechanics (general) (82B05) Quantum equilibrium statistical mechanics (general) (82B10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Related Items (19)

Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field ⋮ Cylindrical Wigner measures ⋮ Concentration of cylindrical Wigner measures ⋮ On the dynamics of the mean-field polaron in the high-frequency limit ⋮ On uniqueness of measure-valued solutions to Liouville's equation of Hamiltonian PDEs ⋮ Norm approximation for the Fröhlich dynamics in the mean-field regime ⋮ Bogoliubov dynamics and higher-order corrections for the regularized Nelson model ⋮ On well-posedness for general hierarchy equations of Gross-Pitaevskii and Hartree type ⋮ Effective potentials generated by field interaction in the quasi-classical limit ⋮ Bohr's Correspondence Principle for the Renormalized Nelson Model ⋮ Ground state properties in the quasiclassical regime ⋮ Quasi-classical ground states. I: Linearly coupled Pauli-Fierz Hamiltonians ⋮ Quasi-classical dynamics ⋮ Semiclassical analysis of quantum asymptotic fields in the Yukawa theory ⋮ Derivation of the Maxwell--Schrödinger Equations from the Pauli--Fierz Hamiltonian ⋮ On some rigorous aspects of fragmented condensation ⋮ On Nelson-type Hamiltonians and abstract boundary conditions ⋮ Infinite dimensional semiclassical analysis and applications to a model in nuclear magnetic resonance ⋮ Self-adjointness criterion for operators in Fock spaces

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