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This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diffusion type… (More)

- A. Arnold
- 2008

We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the existence… (More)

- Maïwenn Beaugrand, A. Arnold, Jérôme Hénin, Dror E. Warschawski, Philip T F Williamson, Isabelle Marcotte
- Langmuir : the ACS journal of surfaces and…
- 2014

Bicelles are model membranes generally made of long-chain dimyristoylphosphatidylcholine (DMPC) and short-chain dihexanoyl-PC (DHPC). They are extensively used in the study of membrane interactions and structure determination of membrane-associated peptides, since their composition and morphology mimic the widespread PC-rich natural eukaryotic membranes. At… (More)

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of… (More)

- A. Arnold, Roberta Bosi, Elayne Zorn
- 2003

This paper is concerned with the well-posedness analysis of the Hartree-Fock system modeling the time evolution of a quantum system comprised of fermions. We consider quantum states with finite mass and finite kinetic energy, and the self-consistent potential is the unbounded Coulomb interaction. This model is first formulated as a semi-linear evolution… (More)

- A. Arnold
- Bulletin of the EATCS
- 1983

This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diiusion type… (More)

- A. Arnold
- 2003

We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global, mass preserving solutions is proved, thus establishing the existence of a… (More)

- A. Arnold
- 2017

In this paper we dérive a hierarchy of absorbing boundary conditions for the Wigner équation of quantum mechanics and model extensions that have been used for semiconductor device simulations For these pseudo-differential équations we analyze the wellposedness of the resulting initial-boundary problems Résumé. — Dans cet article, nous établissons une… (More)

- A. Arnold
- Acta Cybern.
- 1989