{"title":"非抛物型两波段Schrödinger-Poisson问题的数学分析","authors":"O. Morandi","doi":"10.1080/00411450.2014.886591","DOIUrl":null,"url":null,"abstract":"A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"1 1","pages":"133 - 161"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2014.886591","citationCount":"1","resultStr":"{\"title\":\"Mathematical Analysis of a Nonparabolic Two-Band Schrödinger-Poisson Problem\",\"authors\":\"O. Morandi\",\"doi\":\"10.1080/00411450.2014.886591\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.\",\"PeriodicalId\":49420,\"journal\":{\"name\":\"Transport Theory and Statistical Physics\",\"volume\":\"1 1\",\"pages\":\"133 - 161\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/00411450.2014.886591\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transport Theory and Statistical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00411450.2014.886591\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transport Theory and Statistical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00411450.2014.886591","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mathematical Analysis of a Nonparabolic Two-Band Schrödinger-Poisson Problem
A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.
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