In this chapter, we review the recent theory of quantum diffusion models derived from the entropy minimization principle. These models are obtained by taking the moments of a collisional Wigner equation and closing the resulting system of equations by a quantum equilibrium. Such an equilibrium is defined as a minimizer of the quantum entropy subject to local constraints of given moments. We provide a framework to develop this minimization approach. The results of numerical simulations show that these models capture well the various features of quantum transport.
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Degond, P., Gallego, S., Méhats, F., Ringhofer, C. (2008). Quantum Diffusion Models Derived from the Entropy Principle. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds) Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71992-2_6
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DOI: https://doi.org/10.1007/978-3-540-71992-2_6
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