Threshold Singularities of the Spectral Shift Function for a Half-Plane\n Magnetic Hamiltonian

2016/09/22 by Vincent Bruneau, Bruneau, Vincent, Pablo Miranda +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1609.07121

openalex publication_date 2016/09/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We consider the Schr "odinger operator with constant magnetic field defined\non the half-plane with a Dirichlet boundary condition, H₀, and a decaying\nelectric perturbation V. We analyze the spectral density near the Landau\nlevels, which are thresholds in the spectrum of H₀, by studying the Spectral\nShift Function (SSF) associated to the pair (H₀+V,H₀). For perturbations\nof a fixed sign, we estimate the SSF in terms of the eigenvalue counting\nfunction for certain compact operators. If the decay of V is power-like, then\nusing pseudodifferential analysis, we deduce that there are singularities at\nthe thresholds and we obtain the corresponding asymptotic behavior of the SSF.\nOur technique gives also results for the Neumann boundary condition.\n

Related

• Resonances and Spectral Shift Function Singularities for Magnetic Quantum Hamiltonians
• Spectral Properties of a Magnetic Quantum Hamiltonian on a Strip
• Dirichlet and Neumann Eigenvalues for Half-Plane Magnetic Hamiltonians
• Spectrum of the Iwatsuka Hamiltonian at thresholds
• On a quantum Hamiltonian in a unitary magnetic field with axisymmetric potential