Classical limit for the varying-mass Schrodinger equation with random inhomogeneities

JOURNAL OF COMPUTATIONAL PHYSICS

卷:438

Article

Chen, Shi¹  Li, Qin^1,2  Yang, Xu³ 

[1] Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA

[2] Univ Wisconsin Madison, Wisconsin Inst Discovery, Madison, WI 53706 USA

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

关键词: Varying-mass;    Schrodinger equation;    Random inhomogeneities;    Semiclassical limit;    Radiative transfer;   

DOI  :  10.1016/j.jcp.2021.110365

来源: Elsevier

【 摘 要 】

The varying-mass Schrodinger equation (VMSE) has been successfully applied to model electronic properties of semiconductor hetero-structures, for example, quantum dots and quantum wells. In this paper, we consider VMSE with small random heterogeneities, and derive a radiative transfer equation as its asymptotic limit. The main tool is to systematically apply the Wigner transform in the classical regime when the rescaled Planck constant epsilon << 1, and expand the Wigner equation to proper orders of epsilon. As a proof of concept, we numerically compute both VMSE and its limiting radiative transfer equation, and show that their solutions agree well in the classical regime. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free