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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 4, Pages 535–542 (Mi vuu559)

MATHEMATICS

The quasi-levels of the Dirac two-dimensional difference operator in a strip

T. S. Tinyukova

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: In the last decade, topological insulators have been actively studied in the physics literature. Topological insulator is a special type of material that is within the scope of an insulator and conducts electricity on the surface. Topological insulators have interesting physical properties, for example, the topological properties of this material can be stably maintained up to high temperatures. Topological insulators can be used in a wide variety of microelectronic devices ranging from very fast and efficient processors to topological quantum computers. The electron in topological insulators is described by the massless Dirac operator. Such operators in quasi-one-dimensional structures (for example, strips with different boundary conditions) are very interesting not only from a physical, but also from a mathematical point of view, but they are still poorly understood by mathematicians. In this article, we have found the eigenvalues of the Dirac difference operator for a potential of the form $V_0 \delta_{n0}$. We have studied the quasi-levels (eigenvalues and resonances) of the operator in the case of small potentials.

Keywords: Dirac difference operator, resolution, spectrum, quasi-level, eigenvalues, resonance.

DOI: https://doi.org/10.20537/vm160408

Full text: PDF file (205 kB)
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Bibliographic databases:

UDC: 517.958, 530.145.6
MSC: 81Q10, 81Q15

Citation: T. S. Tinyukova, “The quasi-levels of the Dirac two-dimensional difference operator in a strip”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:4 (2016), 535–542

Citation in format AMSBIB
\Bibitem{Tin16} \by T.~S.~Tinyukova \paper The quasi-levels of the Dirac two-dimensional difference operator in a strip \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2016 \vol 26 \issue 4 \pages 535--542 \mathnet{http://mi.mathnet.ru/vuu559} \crossref{https://doi.org/10.20537/vm160408} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3604254} \elib{http://elibrary.ru/item.asp?id=27673739}