2013/12/09 by Ansgar Jüngel, Jüngel, Ansgar, Claudia Negulescu +3
Engineering · Mathematics · Physics and Astronomy · #35K51 #82D37 #Advanced Thermodynamics and Statistical Mechanics #Advancements in Semiconductor Devices and Circuit Design #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics #math.AP #msc:35K51 #msc:82D37
paper · pdf · doi:10.48550/arxiv.1312.2461
arxiv created 2013/12/09 · openalex publication_date 2013/12/09 · arxiv updated 2013/12/10 · openalex created_date 2022/10/06 · openalex updated_date 2026/08/01
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× 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 magnetization. In these variables, the diffusion matrix becomes diagonal. The proofs of the L^∞ 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.