Band functions in the presence of magnetic steps

DOI10.1142/S0218202516500056zbMath1342.35280arXiv1501.02824OpenAlexW1885411807MaRDI QIDQ2788508

Nicolas Popoff, Mikael Persson Sundqvist, Peter D. Hislop, Nicolas Raymond

Publication date: 19 February 2016

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.02824

zbMATH Keywords

magnetic Schrödinger operatorsband functionsedge currents

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic expansions of solutions to PDEs (35C20) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (16)

Eigenvalue asymptotics for a Schrödinger operator with non-constant magnetic field along one direction ⋮ A 3D-Schrödinger operator under magnetic steps with semiclassical applications ⋮ Magnetic quantum currents in the presence of a Neumann wall ⋮ Effective operators on an attractive magnetic edge ⋮ Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential ⋮ Semiclassical eigenvalue estimates under magnetic steps ⋮ Non-homogeneous magnetic permeability and magnetic steps within the Ginzburg-Landau model ⋮ The distribution of superconductivity near a magnetic barrier ⋮ The breakdown of superconductivity in the presence of magnetic steps ⋮ A geometric Iwatsuka type effect in quantum layers ⋮ Spectrum of the Iwatsuka Hamiltonian at thresholds ⋮ The influence of magnetic steps on bulk superconductivity ⋮ Absence of embedded eigenvalues for translationally invariant magnetic Laplacians ⋮ On an extension of the Iwatsuka model ⋮ Lowest energy band function for magnetic steps ⋮ Averaging of magnetic fields and applications

Cites Work

• Edge states induced by Iwatsuka Hamiltonians with positive magnetic fields
• Quantization of edge currents along magnetic barriers and magnetic guides
• Eigenvalues variation. I: Neumann problem for Sturm--Liouville operators
• Examples of absolutely continuous Schrödinger operators in magnetic fields
• Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential
• Some propagation properties of the Iwatsuka model
• On spectral properties of translationally invariant magnetic Schrödinger operators
• Multiple wells in the semi-classical limit I
• Multiple Wells in the Semi-Classical Limit III - Interaction Through Non-Resonant Wells
• ANALYTICITY AND ASYMPTOTIC PROPERTIES OF THE MAXWELL OPERATOR'S DISPERSION CURVES
• Magnetic bottles in connection with superconductivity

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