Quantum Navier-Stokes equations for electrons in graphene

TL;DR

This paper derives quantum Navier-Stokes equations for electrons in graphene using the Chapman-Enskog method and quantum maximum entropy principle, incorporating semiclassical expansion up to second order in Planck's constant.

Contribution

It introduces a novel derivation of quantum Navier-Stokes equations for graphene electrons based on quantum kinetic theory and maximum entropy principles.

Findings

Derived quantum Navier-Stokes equations for graphene electrons

Incorporated semiclassical expansion up to  order in 

Extended previous kinetic models with quantum corrections

Abstract

The Chapman-Enskog method, in combination with the quantum maximum entropy principle, is applied to the Wigner equation in order to obtain quantum Navier-Stokes equations for electrons in graphene in the isothermal case. The derivation is based on the quantum version of the maximum entropy principle and follows the lines of Ringhofer-Degond-M\'ehats' theory (J. Stat. Phys. 112, 2003 and Z. Angew. Math. Mech. 90, 2010). The model obtained in this way is then semiclassically expanded up to $\mathcal{O}(\hbar^2)$.