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14
Quantum energytransport and driftdiffusion models
 J. Stat. Phys
, 2005
"... We show that Quantum EnergyTransport and Quantum DriftDiffusion 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 flu ..."
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Cited by 15 (5 self)
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We show that Quantum EnergyTransport and Quantum DriftDiffusion 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 spatially nonlocal relations. Thanks to an � expansion of these models, � 2 perturbations of the Classical EnergyTransport and DriftDiffusion models are found. In the DriftDiffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the EnergyTransport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic. 1
Quantum hydrodynamic models derived from the entropy principle
, 2004
"... the entropy principle ..."
Energytransport models for charge carriers involving impact ionization in semiconductors
, 2000
"... ..."
Transport of Trapped Particles in a Surface Potential
"... In this paper, we propose a model to describe the transport of trapped particles in a surface potential. It is derived from a microscopic (kinetic) description of particle motion in the potential subject to collisions with the solid surface. Under specific hypotheses on the collision operator and ad ..."
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Cited by 5 (3 self)
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In this paper, we propose a model to describe the transport of trapped particles in a surface potential. It is derived from a microscopic (kinetic) description of particle motion in the potential subject to collisions with the solid surface. Under specific hypotheses on the collision operator and adequate time and space rescaling, the kinetic model is formally shown to converge to a diffusion equation in positionenergy space known in the literature as the SHE model (for Spherical Harmonics Expansion). The model applies to several practical situations in semiconductor and plasma physics. Key words: Botzmann equation, Diffusion equation, Spherical Harmonics Expansion, Semiconductors, Plasmas, Surface collisions. AMS Subject classification: 35Q20, 76P05, 82A70, 78A35, 41A60 Acknowledgements: The author would express his gratitude to J. P. Boeuf for having suggested this problem and provided encouragements and references. This work has been supported by the TMR network No. ERB FMBX CT97 ...
A Scattering Matrix Model of Semiconductor Superlattices in Multidimensional WaveVector Space and Its Diffusion Limit
"... We first establish a quantum microscopic scattering matrix model in multidimensional wavevector space, which relates the phase space density of each superlattice cell with that of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (Spherical Harmonics Expansion)type model ..."
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Cited by 1 (0 self)
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We first establish a quantum microscopic scattering matrix model in multidimensional wavevector space, which relates the phase space density of each superlattice cell with that of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (Spherical Harmonics Expansion)type model of diffusion equations for the particle number density in the positionenergy space is obtained. The crucial features of diffusion constants on retaining the memory of the quantum scattering characteristics of the superlattice elementary cell (like e.g. transmission resonances) are shown in order. Two examples are treated with the analytically computation of the diffusion constants. Key words: superlattices, scattering matrix model, diffusion approximation, spherical harmonics expansion, driftdiffusion, energy transport, transmission resonance.
Mathematical Models for Charge Transport
"... We review a few problems issued from the modeling of the transport of charged particles, subject to the influence of given or selfconsistent electric fields. We describe some of the mathematical methods introduced to deal with these problems. ..."
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We review a few problems issued from the modeling of the transport of charged particles, subject to the influence of given or selfconsistent electric fields. We describe some of the mathematical methods introduced to deal with these problems.
Diffusion limits of kinetic models
"... Summary. This paper reports on recent developments in diffusive limits of kinetic systems. Usually, collision operators in kinetic theory exhibit multiple relaxation scales and before a full relaxation towards a Maxwellian equilibrium has been achieved, the system passes through a series of states t ..."
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Summary. This paper reports on recent developments in diffusive limits of kinetic systems. Usually, collision operators in kinetic theory exhibit multiple relaxation scales and before a full relaxation towards a Maxwellian equilibrium has been achieved, the system passes through a series of states that can be described by partial equilibria. The paper describes various models describing the dynamics of these partial equilibria, namely the SHE (Spherical Harmonics Expansion) and the ET (Energy Transport) models. Various examples of applications of these models to plasma problems are presented. Acknowledgements: Work partially supported by the Commissariat l’Energie Atomique and by Centre National d’Etudes Spatiales