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A. Jüngel, C. Negulescu, P. Shpartko:
"Bounded weak solutions to a matrix drift-diffusion model for spin-coherent electron transport in semiconductors";
Mathematical Models & Methods in Applied Sciences, 25 (2015), 929 - 958.

The global-in-time existence and uniqueness of bounded weak solutions to a spinorial
matrix drift-diffusion model for semiconductors is proved. Developing the electron density
matrix in the Pauli basis, the coefficients (charge density and spin-vector density)
satisfy a parabolic 4 x 4 cross-diffusion system. The key idea of the existence proof is to
work with different variables: the spin-up and spin-down densities as well as the parallel
and perpendicular components of the spin-vector density with respect to the precession
vector. In these variables, the diffusion matrix becomes diagonal. The proofs of the L^\infty
estimates are based on Stampacchia truncation as well as Moser- and Alikakos-type
iteration arguments. The monotonicity of the entropy (or free energy) is also proved.
Numerical experiments in one-space dimension using a finite-volume discretization indicate
that the entropy decays exponentially fast to the equilibrium state.

Siehe englisches Abstract.

Spinorial semiconductors; drift-diffusion

http://dx.doi.org/10.1142/S0218202515500232