Abstract:
We compute the trace formula for the magnetic Laplacian on a compact hyperbolic
surface of constant curvature with a constant magnetic field for energies above the Mane critical
level of the corresponding magnetic geodesic flow. We discuss the asymptotic behavior of the
coefficients of the trace formula when the energy approaches the Mane critical level.
Keywords:
trace formula, magnetic Laplacian, magnetic geodesic flow.
The second author (I.A.T.) was partially supported by the Mathematical Center in Akademgorodok
under the agreement No. 075-15-2022-282 with the Ministry of Science and Higher
Education of the Russian Federation.
Citation:
Yuri A. Kordyukov, Iskander A. Taimanov, “Trace Formula for the Magnetic Laplacian on a Compact
Hyperbolic Surface”, Regul. Chaotic Dyn., 27:4 (2022), 460–476
\Bibitem{KorTai22}
\by Yuri A. Kordyukov, Iskander A. Taimanov
\paper Trace Formula for the Magnetic Laplacian on a Compact
Hyperbolic Surface
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 4
\pages 460--476
\mathnet{http://mi.mathnet.ru/rcd1175}
\crossref{https://doi.org/10.1134/S1560354722040050}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4462433}
Linking options:
https://www.mathnet.ru/eng/rcd1175
https://www.mathnet.ru/eng/rcd/v27/i4/p460
This publication is cited in the following 4 articles:
I. A. Taimanov, “Geometry and quasiclassical quantization of magnetic monopoles”, Theoret. and Math. Phys., 218:1 (2024), 129–144
Yu. A. Kordyukov, “Trace formula for the magnetic Laplacian at zero energy level”, Russian Math. Surveys, 77:6 (2022), 1107–1148
A. V. Bolsinov, V. M. Buchstaber, A. P. Veselov, P. G. Grinevich, I. A. Dynnikov, V. V. Kozlov, Yu. A. Kordyukov, D. V. Millionshchikov, A. E. Mironov, R. G. Novikov, S. P. Novikov, A. A. Yakovlev, “Iskander Asanovich Taimanov (on his 60th birthday)”, Russian Math. Surveys, 77:6 (2022), 1159–1168
Yen-Kheng Lim, “Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry”, Phys. Rev. D, 106:6 (2022)
Citation in format AMSBIB
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