Little Magnetic Book

Abstract

This book is devoted to the spectral analysis of the magnetic Laplacian in various geometric situations. In particular the influence of the geometry on the discrete spectrum is analysed in many asymptotic regimes.

References in corpus (11)

• On the spectrum of curved quantum waveguides
• Leaky Quantum Graphs: A Review
• Asymptotic eigenvalue estimates for a Robin problem with a large parameter
• Magnetic Wells in Dimension Three
• An Improvement on the Brézis-Gallouët technique for 2D NLS and 1D half-wave equation
• Magnetic WKB Constructions
• Contribution to the asymptotic analysis of the Landau-de Gennes functional
• Smooth Homogenization of Heat Equations on Tubular Neighborhoods
• Band functions in the presence of magnetic steps
• Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator
• Resonances and Spectral Shift Function Singularities for Magnetic Quantum Hamiltonians

Cited by in corpus (15)

• On the MIT bag model: self-adjointness and non-relativistic limit
• Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian
• Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells
• A semiclassical Birkhoff normal form for symplectic magnetic wells
• On the spectrum of non degenerate magnetic Laplacian
• Surface Effects in Superconductors with Corners
• A semiclassical Birkhoff normal form for constant-rank magnetic fields
• Asymptotics of Robin eigenvalues on sharp infinite cones
• Spectral asymptotics for $\delta$-interactions on sharp cones
• Effects of Corners in Surface Superconductivity
• Characterization of the traces on the boundary of functions in magnetic Sobolev spaces
• Magnetic field influence on the discrete spectrum of locally deformed leaky wires
• Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle with constant rank curvature
• Agmon-type decay of eigenfunctions for a class of Schrödinger operators with non-compact classically allowed region
• Edge States for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve