Diffusive corrections to asymptotics of a strong-field quantum transport equation

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Manzini, Chiara¹  Frosali, Giovanni¹ 

[1] Univ Florence, Dipartimento Matemat G Sansone, I-50139 Florence, Italy

关键词: Asymptotic analysis;    Quantum drift-diffusion model;    Wigner equation;    Open quantum systems;    Singularly perturbed parabolic equations;   

DOI  :  10.1016/j.physd.2009.10.016

来源: Elsevier

【 摘 要 】

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number epsilon, evolution equations are derived for the terms of zeroth and first order in epsilon. In particular, a quantum drift-diffusion equation for the position density of electrons, with an epsilon-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order epsilon(2), uniformly in time and for arbitrary initial data is given. (c) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free