Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media
文献类型：期刊论文
| 作者 | Cao, Li-qun1 ; Luo, Jian-lan2; Wang, Chong-yu3
|
| 刊名 | APPLIED MATHEMATICS AND COMPUTATION
 |
| 出版日期 | 2010-12-15 |
| 卷号 | 217期号:8页码:3955-3973 |
| 关键词 | Homogenization Multiscale asymptotic expansion Schrodinger equation The effective mass approximation Multiscale finite element method |
| ISSN号 | 0096-3003 |
| DOI | 10.1016/j.amc.2010.10.002 |
| 英文摘要 | In solid state physics, the most widely used techniques to calculate the electronic levels in nanostructures are the effective masses approximation (EMA) and its extension the multiband k.p method (see [9]). They have been particularly successful in the case of heterostructures (see, e. g. [4,9,11]). This paper discusses the multiscale analysis of the Schrodinger equation with rapidly oscillating coefficients. The new contributions obtained in this paper are the determination of the convergence rate for the approximate solutions, the definition of boundary layer solutions, and higher-order correctors. Consequently, a multiscale finite element method and some numerical results are presented. As one of the main results of this paper, we give a reasonable interpretation why the effective mass approximation is very accurate for calculating the band structures in semiconductor in the vicinity of C point, from the viewpoint of mathematics. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved. |
| 资助项目 | National Natural Science Foundation of China[60971121] ; National Natural Science Foundation of China[90916027] ; National Basic Research Program of China (973 Program)[2010CB832702] ; National Basic Research Program of China (973 Program)[2011CB606002] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000284600700029 |
| 出版者 | ELSEVIER SCIENCE INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/10327]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Cao, Li-qun |
| 作者单位 | 1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Beijing Univ Aeronaut & Astronaut, Sch Phys & Nucl Energy Engn, Beijing 100191, Peoples R China 3.Tsinghua Univ, Dept Phys, Beijing 100191, Peoples R China |
| 推荐引用方式 GB/T 7714 | Cao, Li-qun,Luo, Jian-lan,Wang, Chong-yu. Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media[J]. APPLIED MATHEMATICS AND COMPUTATION,2010,217(8):3955-3973. |
| APA | Cao, Li-qun,Luo, Jian-lan,&Wang, Chong-yu.(2010).Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media.APPLIED MATHEMATICS AND COMPUTATION,217(8),3955-3973. |
| MLA | Cao, Li-qun,et al."Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media".APPLIED MATHEMATICS AND COMPUTATION 217.8(2010):3955-3973. |
入库方式： OAI收割
来源：数学与系统科学研究院
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