Review on spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle

DOI10.5802/cml.83zbMath1503.58014OpenAlexW4309784402MaRDI QIDQ2099404

Léo Morin

Publication date: 23 November 2022

Published in: Confluentes Mathematici (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/cml.83

zbMATH Keywords

eigenvalue asymptoticsspectral theorysemiclassical limitBochner Laplacianmagnetic LaplacianWeyl estimates

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Spectral theory and eigenvalue problems for partial differential equations (35Pxx)

Cites Work

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• Magnetic wells in dimension three
• Almost complex structures and geometric quantization
• The spin\(^{\mathbf c}\) Dirac operator on high tensor powers of a line bundle
• Bound states of the magnetic Schrödinger operator
• Geometry and spectrum in 2D magnetic wells
• Spectral methods in surface superconductivity
• Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells
• Semiclassical spectral analysis of the Bochner-Schrödinger operator on symplectic manifolds of bounded geometry
• Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator II: The Case of Degenerate Wells
• Semiclassical spectral asymptotics for a two-dimensional magnetic Schr\"odinger operator: The case of discrete wells
• Trace formula for the magnetic Laplacian
• Semiclassical Spectral Asymptotics for a Magnetic Schrödinger Operator with Non-vanishing Magnetic Field

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