Abstract
We derive some fluid-dynamic models for electron transport near aDirac point in graphene. We start from a kinetic model constitutedby a set of spinorial Wigner equations, we make suitable scalings(hydrodynamic or diffusive) of the model and we build momentequations, which we close through a minimum entropy principle. Inorder to do this we make some assumptions: the usualsemiclassical approximation (ħ $\ll 1$), and two furtherhypothesis, namelyLow Scaled Fermi Speed (LSFS) and Strongly Mixed State (SMS),which allow us to explicitly compute the closure.
Highlights
In the following of this paper we will build two hydrodynamic models for quantum electron transport in graphene following a strategy similar to that one employed in the construction of the diffusive models (42), (55)
In this paper we have proposed four fluid-dynamic models for quantum electron transport in graphene: the first two ones are diffusive-type models, the last two ones are hydrodynamic-type models
All models have been built by using a statistical closure of the moment equations derived from the Wigner system (3) based on the minimization of the quantum entropy functional (12), (13)
Summary
Mathematical models of fluid-dynamic type has been developed in order to describe quantum transport in semiconductors [2, 4, 5, 6, 9, 10, 11, 15, 18]. See [14]), the ad-hoc ansatz (like the Gardner’s equilibrium distribution, see [11]), and a strategy of entropy minimization (which will be followed in this paper, in analogy to the method employed in the closure of classical fluid-dynamic systems derived from the Boltzmann transport equation in the classical statistical mechanics, see [4, 5, 6, 13]). We will consider here a kinetic model for quantum transport in graphene, derived from the one-particle Hamiltonian (2), and we will build four (semiclassical) fluid-dynamic models for the system under consideration: two QDE models and two QHE models.
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