The Hall effect in Lobachevsky space
https://doi.org/10.29235/1561-2430-2023-59-1-71-80
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.
Supporting agencies: The authors thank V. M. Redʼkov for assistance in preparing the manuscript and members of the se- minar of the Center “Fundamental Interactions and Astrophysics” for a helpful discussion.
About the Authors
Yu. A. Kurochkin
B. I. Stepanov Institute of Phy- sics of the National Academy of Sciences of Belarus
Belarus
Belarus
Yurii A. Kurochkin – Dr. Sc. (Physics and Mathe- matics), Professor, Head of the Center “Fundamental Interactions and Astrophysics”
68-2, Nezavisimosti Ave., 220072, Minsk
I. Yu. Rybak
Instituto de Astrofísica e Ciências do Espaço
Portugal
Portugal
Ivan Yu. Rybak – Ph. D. (Physics and Mathematics)
CAUP, Rua das Estrelas, 4150-762 Porto
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