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

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 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.