{"title":"Shape dependent controllability of a quantum transistor","authors":"F. Méhats, Y. Privat, M. Sigalotti","doi":"10.1109/CDC.2013.6760054","DOIUrl":null,"url":null,"abstract":"We investigate the controllability of a quantum electron trapped in a two-dimensional device. The problem is modeled by the Schrödinger equation in a bounded domain coupled to the Poisson equation for the electrical potential. The controller acts on the system through the boundary condition on the potential, on a part of the boundary modeling the gate. We prove that, generically with respect to the shape and boundary conditions on the gate, the device is controllable.","PeriodicalId":415568,"journal":{"name":"52nd IEEE Conference on Decision and Control","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"52nd IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2013.6760054","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the controllability of a quantum electron trapped in a two-dimensional device. The problem is modeled by the Schrödinger equation in a bounded domain coupled to the Poisson equation for the electrical potential. The controller acts on the system through the boundary condition on the potential, on a part of the boundary modeling the gate. We prove that, generically with respect to the shape and boundary conditions on the gate, the device is controllable.
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