44 citations · 132 across the 21 of their papers we have counts for
9 papers · 1 filter
The Schrödinger-Klein-Gordon System Revisited
Christophe Cheverry, Zied Ammari
We introduce a microlocal formulation of the Schr{ö}dinger-Klein-Gordon system describing the interaction between a non-relativistic quantum particle and a Klein-Gordon field throu…
Gibbs measures as local equilibrium KMS states for focusing nonlinear Schrödinger equations
Zied Ammari, Andrew Rout, Vedran Sohinger
In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schrödinger and Hartree equations on the d-dimensional torus when d=1,2,3. Due to th…
Almost sure existence of global solutions for general initial value problems
Zied Ammari, Shahnaz Farhat, Vedran Sohinger
This article is concerned with the almost sure existence of global solutions for initial value problems of the form on separable dual Banach spaces. We prove…
Towards a derivation of Classical ElectroDynamics of charges and fields from QED
Zied Ammari, Marco Falconi, Fumio Hiroshima
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agre…
On well-posedness and uniqueness for general hierarchy equations of Gross-Pitaevskii and Hartree type
Zied Ammari, Quentin Liard, Clément Rouffort
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 t…
On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs
Zied Ammari, Quentin Liard
In this paper, we give a uniqueness result to a transport equation fulfilled by probability measure on a infinite dimensional Hilbert space. Main arguments are based on projective…