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The Wigner Equation

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Transport Equations for Semiconductors

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The quantum mechanical motion of an electron ensemble can be described by the Schrödinger or the density-matrix formulation (see Sect. 10.1). There is an alternative description based on the quantum-kinetic Wigner formalism, which we present and discuss in this chapter. There are two main reasons for using this framework in applications (mostly for transient problems). First, the Wigner picture allows, in contrast to Schrödinger models, for a modeling of scattering phenomena in the form of a quantum Boltzmann equation. Second, the quantum-kinetic framework makes it easier to formulate boundary conditions at the device contacts, which may be inspired from classical kinetic considerations [1]. In this chapter, following [2], we formulate the quantum Liouville equation, the quantum Vlasov equation, and quantum Boltzmann models and discuss their relations to the classical kinetic equations introduced in Chaps. 3 and 4.

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Jüngel, A. (2009). The Wigner Equation. In: Transport Equations for Semiconductors. Lecture Notes in Physics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89526-8_11

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  • DOI: https://doi.org/10.1007/978-3-540-89526-8_11

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