Abstract
Starting from the Liouville–von Neumann equation of motion for the density matrix of a system of electrons and phonons, we derive a Master Equation valid over short length-scales by treating the phonons as first-order perturbations. In so doing, we show how elusive is the Ansatz required to introduce irreversibility. We then show how the Boltzmann transport equation is obtained over much longer length-scales by “patching” short sections together and incoherently. We discuss all of the assumptions required to reach this result and consider also interactions with ionized impurities and the case of interacting electrons.
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Fischetti, M.V., Vandenberghe, W.G. (2016). *From Liouville—von Neumann to Boltzmann: The Semiclassical Limit. In: Advanced Physics of Electron Transport in Semiconductors and Nanostructures. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-01101-1_18
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DOI: https://doi.org/10.1007/978-3-319-01101-1_18
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