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

Borthwick, David; Uribe, Alejandro

doi:10.1090/S0002-9947-06-04197-3

The semiclassical structure of low-energy states in the presence of a magnetic field
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by David Borthwick and Alejandro Uribe PDF

Trans. Amer. Math. Soc. 359 (2007), 1875-1888 Request permission

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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