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
Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution. / Gevorgyan, Eva; Nersessian, Armen; Ohanyan, Vadim; Tolkachev, Evgeny.
In: Modern Physics Letters A, Vol. 29, No. 29, 1450148, 21.09.2014.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:84929578190
VL - 29
JO - Modern Physics Letters A
JF - Modern Physics Letters A
SN - 0217-7323
IS - 29
M1 - 1450148
ER -