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We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through… (More)

- Naoufel Ben Abdallah, Florian Méhats, Christian Schmeiser, Rada-Maria Weishäupl
- SIAM J. Math. Analysis
- 2005

The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A… (More)

In this work, we give an overview of recently derived quantum hydrodynamic and diffusion models. A quantum local equilibrium is defined as a minimizer of the quantum entropy subject to local moment constraints (such as given local mass, momentum and energy densities). These equilibria relate the thermodynamic parameters (such as the temperature or chemical… (More)

- Naoufel Ben Abdallah, Florian Méhats, Olivier Pinaud
- SIAM J. Math. Analysis
- 2005

Asymptotic quantum transport models of a two-dimensional electron gas are presented. The starting point is a singular perturbation of the threedimensional Schrödinger-Poisson system. The small parameter ε is the scaled width of the electron gas and appears as the lengthscale on which a one dimensional confining potential varies. The rigorous ε→ 0 limit is… (More)

Abstract Weak solutions of a Vlasov-Schrödinger-Poisson system are shown to exist in the stationary and time-dependent situations. This system models the transport and interaction of electrons in a bidimensional electron gas. The particles are assumed to have a wave behaviour in the confinement directions (z) and to behave like point particles in the… (More)

- Nicolas Crouseilles, Mohammed Lemou, Florian Méhats
- J. Comput. Physics
- 2013

- Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats
- Numerische Mathematik
- 2015

This work is devoted to the numerical simulation of nonlinear Schrödinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency. This is a stronger feature than the usual so called “Asymptotic preserving” property, the last being also satisfied by our… (More)

- Samy Gallego, Florian Méhats
- SIAM J. Numerical Analysis
- 2005

This paper is devoted to the discretization and numerical simulation of a new quantum drift-diffusion model that was recently derived. In a first step, we introduce an implicit semi-discretization in time which possesses some interesting properties: this system is well-posed, it preserves the positivity of the density, the total charge is conserved, and it… (More)

A selfconsistent model for charged particles, accounting for quantum confinement, diffusive transport and electrostatic interaction is considered. The electrostatic potential is a solution of a three dimensional Poisson equation with the particle density as the source term. This density is the product of a two dimensional surface density and that of a one… (More)

and σN is the area of the unit sphere in R (σ3 = 4π and σ4 = 2π). This nonlinear transport equation describes in dimension N = 3 the mechanical state of a stellar system subject to its own gravity (see for instance [3, 14]). Classical calculations show that this model should be correct only for low velocities, and if high velocities occur, special… (More)