### Abstract

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 language | English |
---|---|

Article number | 1450148 |

Journal | Modern Physics Letters A |

Volume | 29 |

Issue number | 29 |

DOIs | |

Publication status | Published - 21 Sep 2014 |

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### Keywords

- Hamilton-Jacobi method
- Landau problem
- Magnetic monopoles

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Nuclear and High Energy Physics

### Cite this

*Modern Physics Letters A*,

*29*(29), [1450148]. https://doi.org/10.1142/S021773231450148X

**Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution.** / Gevorgyan, Eva; Nersessian, Armen; Ohanyan, Vadim; Tolkachev, Evgeny.

Research output: Contribution to journal › Article

*Modern Physics Letters A*, vol. 29, no. 29, 1450148. https://doi.org/10.1142/S021773231450148X

}

TY - JOUR

T1 - Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

AU - Gevorgyan, Eva

AU - Nersessian, Armen

AU - Ohanyan, Vadim

AU - Tolkachev, Evgeny

PY - 2014/9/21

Y1 - 2014/9/21

N2 - 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.

AB - 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.

KW - Hamilton-Jacobi method

KW - Landau problem

KW - Magnetic monopoles

UR - http://www.scopus.com/inward/record.url?scp=84929578190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929578190&partnerID=8YFLogxK

U2 - 10.1142/S021773231450148X

DO - 10.1142/S021773231450148X

M3 - Article

VL - 29

JO - Modern Physics Letters A

JF - Modern Physics Letters A

SN - 0217-7323

IS - 29

M1 - 1450148

ER -