Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

Eva Gevorgyan, Armen Nersessian, Vadim Ohanyan, Evgeny Tolkachev

    Research output: Contribution to journalArticlepeer-review


    We define the Landau problem on two-dimensional ellipsoid, hyperboloid and paraboloid of revolution. Starting from the two-center McIntosh-Cisneros-Zwanziger (MICZ)-Kepler system and making the reduction into these two-dimensional surfaces, we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution in the magnetic field conserving the symmetry of the two-dimensional surface (Landau problem). For each case we figure out the values of parameter for which the qualitative character of the motion coincides with that of a free particle moving on the same two-dimensional surface. For the case of finite trajectories we construct the action-angle variables.

    Original languageEnglish
    Article number1450148
    JournalModern Physics Letters A
    Issue number29
    Publication statusPublished - 21 Sep 2014


    • Hamilton-Jacobi method
    • Landau problem
    • Magnetic monopoles

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Nuclear and High Energy Physics

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