Communications in Mathematical Sciences

Volume 11 (2013)

Number 3

Two spinorial drift-diffusion models for quantum electron transport in graphene

Pages: 807 – 830



Ansgar Jüngel (Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien, Austria)

Nicola Zamponi (Dipartimento di Matematica Ulisse Dini, Firenze, Italy)


Two drift-diffusion models for the quantum transport of electrons in graphene, which account for the spin degree of freedom, are derived from a spinorial Wigner equation with relaxation-time or mass- and spin-conserving matrix collision operators using a Chapman-Enskog expansion around the thermal equilibrium. Explicit models are computed by assuming that both the semiclassical parameter and the scaled Fermi energy are sufficiently small. For one of the models, the global existence of weak solutions, entropy-dissipation properties, and the exponential long-time decay of the spin vector are proved. Finally, numerical simulations of a one-dimensional ballistic diode using both models are presented, showing the temporal behavior of the particle density and the components of the spin vector.


Wigner equation, semiclassical limit, Chapman-Enskog expansion, spinorial drift-diffusion equations, existence of solutions, long-time behavior of solutions, entropy dissipation, graphene

2010 Mathematics Subject Classification

35B40, 35K51, 82D37

Published 14 May 2013