Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle with constant rank curvature

2020/10/01 by Morin, Léo
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2010.00226

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.

Related

• Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a\n positive line bundle on a symplectic manifold
• Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions
• Resolvents of Bochner Laplacians in the semiclassical limit
• Little Magnetic Book
• Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field