{"title":"The Hall effect in Lobachevsky space","authors":"Y. Kurochkin, I. Rybak","doi":"10.29235/1561-2430-2023-59-1-71-80","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the problem of the classical and quantum movement of a charged particle in a two-dimensional Lobachevsky space in the presence of analogues of uniform magnetic and electric fields. Based on this consideration, equations for the conductivity for the classical and quantum Hall effect are obtained. It is shown that in Lobachevsky space the presence of a small electrical field leads to a shift of the stair structure of the quantum Hall conductivity.","PeriodicalId":20584,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus, Medical series","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences of Belarus, Medical series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-2430-2023-59-1-71-80","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Medicine","Score":null,"Total":0}
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Abstract
In this paper, we consider the problem of the classical and quantum movement of a charged particle in a two-dimensional Lobachevsky space in the presence of analogues of uniform magnetic and electric fields. Based on this consideration, equations for the conductivity for the classical and quantum Hall effect are obtained. It is shown that in Lobachevsky space the presence of a small electrical field leads to a shift of the stair structure of the quantum Hall conductivity.
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