71 citations · 176 across the 14 of their papers we have counts for
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Nonlinear instability of inhomogeneous steady states solutions to the HMF Model
Mohammed Lemou, Ana Maria Luz, Florian Méhats
In this work we prove the nonlinear instability of inhomogeneous steady states solutions to the Hamiltonian Mean Field (HMF) model. We first study the linear instability of this mo…
Stable Ground States for the HMF Poisson Model
Marine Fontaine, Mohammed Lemou, Florian Méhats
In this paper we prove the nonlinear orbital stability of a large class of steady states solutions to the Hamiltonian Mean Field (HMF) system with a Poisson interaction potential.…
Uniformly accurate time-splitting methods for the semiclassical Schrödinger equation Part 1 : Construction of the schemes and simulations
Philippe Chartier, Loïc Le Treust, Florian Méhats
This article is devoted to the construction of new numerical methods for the semiclassical Schrödinger equation. A phase-amplitude reformulation of the equation is described where…
Uniformly accurate time-splitting methods for the semiclassical linear Schr{ö}dinger equation
Philippe Chartier, Loïc Le Treust, Florian Méhats
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{ö}dinger equation in t…
The quantum Liouville-BGK equation and the moment problem
Florian Méhats, Olivier Pinaud
This work is devoted to the analysis of the quantum Liouville-BGK equation. This equation arises in the work of Degond and Ringhofer on the derivation of quantum hydrodynamical mod…
Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime
Weizhu Bao, Loïc Le Treust, Florian Méhats
We study dimension reduction for the three-dimensional Gross-Pitaevskii equation with a long-range and anisotropic dipole-dipole interaction modeling dipolar Bose-Einstein condensa…
Analysis of models for quantum transport of electrons in graphene layers
Raymond El Hajj, Florian Méhats
We present and analyze two mathematical models for the self consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can mo…