vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2023-59-1-71-80vestifm-704Research ArticleФИЗИКАPHYSICSЭффект Холла в пространстве ЛобачевскогоThe Hall effect in Lobachevsky spaceКурочкинЮ. А.KurochkinYu. A.

Курочкин Юрий Андреевич – доктор физико-математических наук, профессор, заведующий центром «Фундаментальные взаимодействия и астрофизика»

пр. Независимости, 68-2, 220072, Минск

Yurii A. Kurochkin – Dr. Sc. (Physics and Mathe- matics), Professor, Head of the Center “Fundamental Interactions and Astrophysics”

68-2, Nezavisimosti Ave., 220072, Minsk

yukuroch@dragon.bas-net.byРыбакИ. Ю.RybakI. Yu.

Рыбак Иван Юрьевич – Институт астрофизики и космических наук 

CAUP, Rua das Estrelas, 4150-762 Porto

Ivan Yu. Rybak – Ph. D. (Physics and Mathematics)

CAUP, Rua das Estrelas, 4150-762 Porto

Ivan.Rybak@astro.up.ptИнститут физики имени Б. И. Степанова Национальной академии наук БеларусиB. I. Stepanov Institute of Phy- sics of the National Academy of Sciences of BelarusИнститут астрофизики и космических наукInstituto de Astrofísica e Ciências do Espaço2023030420235917180Copyright © Курочкин Ю.А., Рыбак И.Ю., 20232023Курочкин Ю.А., Рыбак И.Ю.Kurochkin Y.A., Rybak I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/704

Рассмотрена задача классического и квантового движения заряженной частицы в двумерном пространстве Лобачевского при наличии аналогов однородного магнитного и электрического полей. На ее основе получены выражения для проводимости классического и квантового эффекта Холла. Показано, что в пространстве Лобачевского наличие небольшого электрического поля приводит к смещению ступенчатой структуры квантовой проводимости Холла.

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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The authors declare that there are no conflicts of interest present.