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Fundam. Prikl. Mat., 2015, Volume 20, Issue 2, Pages 5–20 (Mi fpm1637)  

This article is cited in 1 scientific paper (total in 1 paper)

Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential

A. Yu. Anikina, J. Brüningb, S. Yu. Dobrokhotovca

a Moscow Institute of Physics and Technology
b Humboldt University, Berlin, Germany
c Institute for Problems in Mechanics of the Russian Academy of Sciences

Abstract: We consider a $2$-dimensional Hamiltonian system describing classical electron motion in a graphene placed in a large constant magnetic field and an electric field with a periodic potential. Using the Maupertuis–Jacobi correspondence and an assumption that the magnetic field is large, we make averaging and reduce the original system to a $1$-dimensional Hamiltonian system on the torus. This allows us to describe the trajectories of both systems and classify them by means of Reeb graphs.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-0052
12-01-00441
Ministry of Education and Science of the Russian Federation НШ-2964.2014.1
Deutsche Forschungsgemeinschaft 647


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English version:
Journal of Mathematical Sciences (New York), 2017, 223:6, 656–666

Bibliographic databases:

UDC: 517.928.7+517.984.5

Citation: A. Yu. Anikin, J. Brüning, S. Yu. Dobrokhotov, “Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential”, Fundam. Prikl. Mat., 20:2 (2015), 5–20; J. Math. Sci., 223:6 (2017), 656–666

Citation in format AMSBIB
\Bibitem{AniBruDob15}
\by A.~Yu.~Anikin, J.~Br\"uning, S.~Yu.~Dobrokhotov
\paper Averaging and trajectories of a~Hamiltonian system appearing in graphene placed in a~strong magnetic field and a~periodic potential
\jour Fundam. Prikl. Mat.
\yr 2015
\vol 20
\issue 2
\pages 5--20
\mathnet{http://mi.mathnet.ru/fpm1637}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3472265}
\elib{https://elibrary.ru/item.asp?id=25686559}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 223
\issue 6
\pages 656--666
\crossref{https://doi.org/10.1007/s10958-017-3375-7}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirozzi, “Scalarization of stationary semiclassical problems for systems of equations and its application in plasma physics”, Theoret. and Math. Phys., 193:3 (2017), 1761–1782  mathnet  crossref  crossref  adsnasa  isi  elib
  • Фундаментальная и прикладная математика
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