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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: David Borthwick and Alejandro Uribe
Journal: Trans. Amer. Math. Soc. 359 (2007), 1875-1888
MSC (2000): Primary 81Q20; Secondary 81S10
Published electronically: November 22, 2006
MathSciNet review: 2272153
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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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Additional Information

David Borthwick
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: davidb@math.emory.edu

Alejandro Uribe
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: uribe@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04197-3
PII: S 0002-9947(06)04197-3
Received by editor(s): February 15, 2005
Published electronically: November 22, 2006
Additional Notes: The first author was supported in part by NSF grant DMS-0204985.
The second author was supported in part by NSF grant DMS-0070690.
Article copyright: © Copyright 2006 American Mathematical Society