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The semiclassical structure of low-energy states in the presence of a magnetic field
Author(s):
David
Borthwick;
Alejandro
Uribe
Journal:
Trans. Amer. Math. Soc.
359
(2007),
1875-1888.
MSC (2000):
Primary 81Q20;
Secondary 81S10
Posted:
November 22, 2006
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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:
10.1090/S0002-9947-06-04197-3
PII:
S 0002-9947(06)04197-3
Received by editor(s):
February 15, 2005
Posted:
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.
Copyright of article:
Copyright
2006,
American Mathematical Society
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