Trace formula for the magnetic Laplacian on a compact hyperbolic surface

DOI10.1134/S1560354722040050arXiv2202.06055WikidataQ113782157 ScholiaQ113782157MaRDI QIDQ6390916

Publication date: 12 February 2022

Abstract: We compute the trace formula for the magnetic Laplacian on a compact hyperbolic surface of constant curvature with 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.

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Perturbations of PDEs on manifolds; asymptotics (58J37) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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