Holomorphic spectral geometry of magnetic Schrödinger operators on Riemann surfaces

DOI10.1016/j.difgeo.2005.09.001zbMath1172.58010OpenAlexW2151311433WikidataQ115357909 ScholiaQ115357909MaRDI QIDQ2490927

Yanyan Li

Publication date: 18 May 2006

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2005.09.001

zbMATH Keywords

elliptic operatorspectral geometryBochner LaplacianHolomorphic line bundle

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10)

Related Items (13)

On the geometry of the energy operator in quantum mechanics ⋮ Unnamed Item ⋮ Magneto-metric Hamiltonians on quantum surfaces in the configuration space ⋮ Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces ⋮ Theta functions and adiabatic curvature on an abelian variety ⋮ The geometry of real reducible polarizations in quantum mechanics ⋮ Fourier-Mukai transform and adiabatic curvature of spectral bundles for Landau Hamiltonians on Riemann surfaces ⋮ Fractional quantum numbers via complex orbifolds ⋮ Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces ⋮ On the spectrum of the twisted Dolbeault Laplacian over Kähler manifolds ⋮ Geometric dynamics on quantum nano-surfaces and low-energy spectrum in a homogeneous magnetic field ⋮ Theta functions and adiabatic curvature on an elliptic curve ⋮ Fractional quantum numbers, complex orbifolds and noncommutative geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Isospectral connections on line bundles
• Spectrum of the Schrödinger operator on a line bundle over complex projective spaces
• Geometric quantization and quantum mechanics
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. III
• On the cohomology of Fuchsian groups
• Fourier coefficients of the resolvent for a Fuchsian group.
• Spectral theory and Fuchsian groups
• Quantization of a particle in a background Yang–Mills field
• Quantization and spectral geometry of a rigid body in a magnetic monopole field

This page was built for publication: Holomorphic spectral geometry of magnetic Schrödinger operators on Riemann surfaces