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
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.
PDF file (202 kB)
Journal of Mathematical Sciences (New York), 2017, 223:6, 656–666
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
\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.
\jour J. Math. Sci.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
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
|Number of views:|