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Quantum Diffusive Higher-Order Moment Equations

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

The strategy of the previous chapter to derive quantum drift-diffusion equations can be generalized. Similar to the semi-classical diffusive limit, we impose several moment constraints, leading to a system of diffusive equations. In this chapter, we explain the general strategy and consider in more detail a specific quantum model, consisting of the balance equations of mass and energy, the so-called quantum energy-transport equations.

Keywords

  • Boltzmann Equation
  • Wigner Function
  • Moment Equation
  • Previous Chapter
  • Entropic Structure

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References

  1. P. Degond, F. Méhats, and C. Ringhofer. Quantum energy-transport and drift-diffusion models. J. Stat. Phys. 118 (2005), 625–665.

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  2. P. Degond, S. Gallego, and F. Méhats. On quantum hydrodynamic and quantum energy transport models. Commun. Math. Sci. 5 (2007), 887–908.

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Correspondence to Ansgar Jüngel .

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© 2009 Springer-Verlag Berlin Heidelberg

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Jüngel, A. (2009). Quantum Diffusive Higher-Order Moment 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_13

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  • DOI: https://doi.org/10.1007/978-3-540-89526-8_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89525-1

  • Online ISBN: 978-3-540-89526-8

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