Geometry and Spectrum in 2D Magnetic Wells
Annales de l'Institut Fourier, Volume 65 (2015) no. 1, p. 137-169

This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in 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.

Cet article est consacré à la mécanique classique et l’analyse spectrale d’un hamiltonien purement magnétique dans 2 . On démontre que la dynamique et la théorie spectrale semi-classique peuvent être traitées par une forme normale de Birkhoff, et ainsi réduites à l’étude d’une famille d’hamiltoniens à un degré de liberté. Corollairement, on obtient une extension de résultats récents de Helffer et Kordyukov à de plus hautes énergies.

DOI : https://doi.org/10.5802/aif.2927
Classification:  81Q20,  35Pxx,  35S05,  70Hxx,  37Jxx
Keywords: magnetic field, normal form, spectral theory, semiclassical limit, Hamiltonian flow, microlocal analysis
@article{AIF_2015__65_1_137_0,
     author = {Raymond, Nicolas and V\~u Ng\d oc, San},
     title = {Geometry and Spectrum  in 2D Magnetic Wells},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {1},
     year = {2015},
     pages = {137-169},
     doi = {10.5802/aif.2927},
     zbl = {1327.81207},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2015__65_1_137_0}
}
Raymond, Nicolas; Vũ Ngọc, San. Geometry and Spectrum  in 2D Magnetic Wells. Annales de l'Institut Fourier, Volume 65 (2015) no. 1, pp. 137-169. doi : 10.5802/aif.2927. http://www.numdam.org/item/AIF_2015__65_1_137_0/

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