Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle with constant rank curvature
Abstract
The goal of this paper is manyfold. Firstly, we want to give a short introduction to the Bochner Laplacian and explain why it acts locally as a magnetic Laplacian. Secondly, given a confining magnetic field, we use Agmon-like estimates to reduce its spectral study to magnetic Laplacians, in the semiclassical limit. Finally, we use this to translate already-known spectral asymptotics for the magnetic Laplacian to the Bochner Laplacian.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.00226
- arXiv:
- arXiv:2010.00226
- Bibcode:
- 2020arXiv201000226M
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Mathematics - Complex Variables;
- Mathematics - Spectral Theory