A semiclassical Birkhoff normal form for symplectic magnetic wells

2019/07/08 by Léo Morin, Morin, Léo
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1907.03493

openalex publication_date 2019/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct a Birkhoff normal form for a semiclassical magnetic Schrödinger operator with non-degenerate magnetic field, and discrete magnetic well, defined on an even dimensional riemannian manifold M. We use this normal form to get an expansion of the first eigenvalues in powers of h^1/2, and semiclassical Weyl asymptotics for this operator.

Citations

• Symplectic manifolds and their lagrangian submanifolds

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