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A quantum-transport model for semiconductors: The Wigner-Poisson problem on a bounded Brillouin zone. (English) Zbl 0742.35046
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:
35Q40 PDEs in connection with quantum mechanics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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