Quantum Navier–Stokes equations for electrons in graphene

The Chapman–Enskog method, in combination with the quantum maximum entropy principle (QMEP), 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–Méhats' 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 O(h^2).