The semiclassical structure of low-energy states in the presence of a magnetic field |
| |
Authors: | David Borthwick Alejandro Uribe |
| |
Institution: | Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322 ; Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 |
| |
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. |
| |
Keywords: | |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 |