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Quantum Hydrodynamic Equations

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Part of the Lecture Notes in Physics book series (LNP,volume 773)

In the previous chapters, we have derived quantum macroscopic models from a Wigner–Boltzmann equation using a diffusion scaling. In this chapter, we show that, in analogy to the semi-classical situation, quantum hydrodynamic models can be derived by employing a hydrodynamic scaling. We present two derivations: one from the (mixed-state) Schrödinger equation and one from a Wigner–Boltzmann equation. This approach can be extended to general quantum moment hydrodynamics, presented in the final section.

Keywords

  • Boltzmann Equation
  • Hydrodynamic Equation
  • Moment Equation
  • Collision Operator
  • Resonant Tunneling Diode

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Correspondence to Ansgar Jüngel .

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Jüngel, A. (2009). Quantum Hydrodynamic Equations. In: Transport Equations for Semiconductors. Lecture Notes in Physics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89526-8_14

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  • DOI: https://doi.org/10.1007/978-3-540-89526-8_14

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