Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

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 Hamiltonia...

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Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Gevorgyan, Eva, Nersessian, Armen, Ohanyan, Vadim, Tolkachev, Evgeny
Format: Article
Language:English
Subjects:
Charged particles
Parabolic bodies
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1304.3221