Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization

Nicola Zamponi

doi:10.3934/krm.2012.5.203

Article Contents

2012, Volume 5, Issue 1: 203-221. Doi: 10.3934/krm.2012.5.203

This issue Previous Article H-Theorem for nonlinear regularized 13-moment equations in kinetic gas theory Next Article

Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization

Nicola Zamponi^1,

1.
Dipartimento di matematica Ulisse Dini, Viale Morgagni 67/A, Firenze

Received: April 30, 2011

Revised: July 31, 2011

Published: February 2012

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Abstract

We derive some fluid-dynamic models for electron transport near a Dirac point in graphene. We start from a kinetic model constituted by a set of spinorial Wigner equations, we make suitable scalings (hydrodynamic or diffusive) of the model and we build moment equations, which we close through a minimum entropy principle. In order to do this we make some assumptions: the usual semiclassical approximation (ħ $\ll 1$), and two further hypothesis, namely Low Scaled Fermi Speed (LSFS) and Strongly Mixed State (SMS), which allow us to explicitly compute the closure.

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Mathematics Subject Classification: Primary: 35Q40, 76Y05; Secondary: 82D37.

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