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Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential

We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions.… Expand

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

- Z. Ammari
- Mathematics
- 1 September 2000

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure… Expand

Mean Field Limit for Bosons and Infinite Dimensional Phase-Space Analysis

Abstract.This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these… Expand

Mean field limit for bosons and propagation of Wigner measures

We consider the N-body Schrodinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., “Mean field limit for… Expand

Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model

- Z. Ammari, M. Falconi
- Physics
- 9 February 2016

This paper studies the derivation of the nonlinear system of Schrodinger--Klein--Gordon (S-KG) equations, coupled by a Yukawa-type interaction, from a microscopic quantum field model of nonrelativi...

Propagation of chaos for many-boson systems in one dimension with a point pair-interaction

- Z. Ammari, S. Breteaux
- PhysicsAsymptot. Anal.
- 17 June 2009

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Wigner Measures Approach to the Classical Limit of the Nelson Model: Convergence of Dynamics and Ground State Energy

- Z. Ammari, M. Falconi
- Physics, Mathematics
- 10 March 2014

We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled… Expand

On Well-Posedness for General Hierarchy Equations of Gross–Pitaevskii and Hartree Type

- Z. Ammari, Q. Liard, C. Rouffort
- Mathematics
- 28 July 2020

Gross–Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs emerging naturally from the mean field theory of Bose gases. Their solutions are known to be related to initial value… Expand

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