Geometry and Spectrum in 2D Magnetic Wells

Nicolas Raymond, San Vũ Ngọc
2015 Annales de l'Institut Fourier  
This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in R 2 . It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form and reduced to the study of a family of one dimensional Hamiltonians. As a corollary, recent results by Helffer-Kordyukov are extended to higher energies.
doi:10.5802/aif.2927 fatcat:ohg2nakkojgg5euuckda22q33e