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Quantum electronic transport in graphene: A kinetic and fluid‐dynamic approach
Author(s) -
Zamponi N.,
Barletti L.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1403
Subject(s) - semiclassical physics , mathematics , graphene , quantum , kinetic energy , closure (psychology) , dirac (video compression format) , statistical physics , mathematical physics , classical mechanics , physics , quantum mechanics , economics , neutrino , market economy
We derive a fluid‐dynamic model for electron transport near a Dirac point in graphene. Starting from a kinetic model, based on spinorial Wigner functions, the derivation of the fluid model is based on the minimum entropy principle, which is exploited to close the moment system deduced from the Wigner equation. To this aim we make two main approximations: the usual semiclassical approximation ( ħ ≪1) and a new one, namely, the ‘strongly mixed state’ approximation, which allow to compute the closure explicitly. Particular solutions of the fluid‐dynamic equations are discussed which are of physical interest because of their connection with the Klein paradox phenomenon. Copyright © 2010 John Wiley & Sons, Ltd.