Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution
Abstract
We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellipsoid, hyperboloid and paraboloid. We start form the two-center MICZ-Kepler system Hamiltonian and then making the reduction into the various two-dimensional surfaces listed above we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution with the magnetic filed conserving the symmetry of the two-dimensional surface(Landau problem). For each case we figure out at which values of parameters the qualitative character of the moving coincides with that of a free particle moving on the save two-dimensional surface. For the case of finite trajectories (ellipsoid) we construct also the action-angle variables.
Keywords
Cite
@article{arxiv.1304.3221,
title = {Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution},
author = {Eva Gevorgyan and Armen Nersessian and Vadim Ohanyan and Evgeny Tolkachev},
journal= {arXiv preprint arXiv:1304.3221},
year = {2014}
}
Comments
11 pages, revised version