The semiclassical structure of low-energy states in the presence of a magnetic field

David Borthwick; Alejandro Uribe

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The semiclassical structure of low-energy states in the presence of a magnetic field

David Borthwick·Alejandro Uribe

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Abstract

We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We demonstrate that the orthogonal projectors onto these states are the Fourier components of an operator with the structure of the Szegö projector, i.e. a Fourier integral operator of Hermite type. This result yields semiclassical asymptotics for the low-energy eigenstates.

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David Borthwick, Alejandro Uribe. 2004-12-11. The semiclassical structure of low-energy states in the presence of a magnetic field. https://arxiv.org/abs/math/0412223

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