Geometry and Spectrum in 2D Magnetic Wells

Nicolas Raymond; San Vu Ngoc

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arXiv · 1306.5054

Geometry and Spectrum in 2D Magnetic Wells

Nicolas Raymond·San Vu Ngoc

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Abstract

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.

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Nicolas Raymond, San Vu Ngoc. 2013-06-21. Geometry and Spectrum in 2D Magnetic Wells. https://arxiv.org/abs/1306.5054

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