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Two spinorial drift-diffusion models for quantum electron transport in graphene. (English) Zbl 1282.35132

Summary: 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.

MSC:

35D30 Weak solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
82D37 Statistical mechanics of semiconductors
78A35 Motion of charged particles
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