Averaging and Trajectories of a Hamiltonian System Appearing in Graphene Placed in a Strong Magnetic Field and a Periodic Potential

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 perform avera...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-06, Vol.223 (6), p.656-666
Main Authors: Anikin, A., Brüning, J., Dobrokhotov, S. Yu
Format: Article
Language:English
Subjects:
Graphene
Hamiltonian functions
Magnetic fields
Mathematics
Mathematics and Statistics
Toruses
Trajectories
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Summary: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 perform 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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-017-3375-7