Large-time asymptotics for a matrix spin drift-diffusion model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Holzinger, Philipp¹  Jungel, Ansgar¹ 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

关键词: Spin-polarized transport in semiconductors;    Drift-diffusion equations;    Density matrix;    Exponential decay;    Large-time asymptotics;    Free energy;   

DOI  :  10.1016/j.jmaa.2020.123887

来源: Elsevier

【 摘 要 】

The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet boundary conditions. If the relaxation time is sufficiently small and the boundary data is close to the equilibrium state, the density matrix converges exponentially fast to the spinless near-equilibrium steady state. The proof is based on a reformulation of the matrix-valued cross-diffusion equations using spin-up and spin-down densities as well as the perpendicular component of the spin-vector density, which removes the cross-diffusion terms. Key elements of the proof are time-uniform positive lower and upper bounds for the spin-up and spin-down densities, derived from the De Giorgi-Moser iteration method, and estimates of the relative free energy for the spin-up and spin-down densities. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free