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

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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.
15 pages

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Spectral Theory, Differential Geometry, 58J50

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http://salesiana.dossiersoluciones.com/handle/123456789/73557

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0412223
 http://arxiv.org/abs/math/0412223

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arXiv