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Zbl 0742.35046
Degond, Pierre; Markowich, Peter A.
A quantum-transport model for semiconductors: The Wigner-Poisson problem on a bounded Brillouin zone. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 24, No.6, 697-709 (1990). ISSN 0764-583X

Summary: We analyse a quantum-mechanical model for the transport of electrons in semiconductors. The model consists of the quantum Liouville (Wigner) equation posed on the bounded Brillouin zone corresponding to the semiconductor crystal lattice, with a self-consistent potential determined by a Poisson equation. A global existence and uniqueness proof for this model is the main result of the paper.

MSC 2000:: *35Q40 PDE from quantum mechanics
35A05 General existence and uniqueness theorems (PDE)

Keywords: quantum Liouville equation; transport of electrons in semiconductors; semiconductor crystal lattice; self-consistent potential; Poisson equation; global existence; uniqueness

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