Eigenvalue Asymptotics in a Twisted Waveguide

DOI10.1080/03605300902892337zbMath1195.35119arXiv0808.1528OpenAlexW2964059203MaRDI QIDQ3643215

Hynek Kovařík, Eric Soccorsi, Philippe Briet, Georgi D. Raikov

Publication date: 10 November 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.1528

zbMATH Keywords

spectral propertiesDirichlet Laplacianeffective masstwisted waveguidesasymptotic term

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (21)

Influence of bounded states in the Neumann Laplacian in a thin waveguide ⋮ Spectral asymptotics of the Dirichlet Laplacian on a generalized parabolic layer ⋮ Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps ⋮ Spectral analysis of sheared nanoribbons ⋮ Scattering in twisted waveguides ⋮ Eigenvalue counting function for Robin Laplacians on conical domains ⋮ Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides ⋮ On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes ⋮ The Hardy inequality and the heat equation in twisted tubes ⋮ Discrete spectrum of quantum Hall effect Hamiltonians. I: Monotone edge potentials ⋮ Resonances near thresholds in slightly twisted waveguides ⋮ Spectrum of the Dirichlet Laplacian in sheared waveguides ⋮ Lifshits tails for randomly twisted quantum waveguides ⋮ An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain ⋮ Eigenvalue and resonance asymptotics in perturbed periodically twisted tubes: twisting versus bending ⋮ On Norm Resolvent and Quadratic Form Convergences in Asymptotic Thin Spatial Waveguides ⋮ Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity ⋮ Dirichlet Laplacian in a thin twisted strip ⋮ Planar waveguide with “twisted” boundary conditions: Discrete spectrum ⋮ On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current ⋮ Hardy inequalities in globally twisted waveguides

Cites Work

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• Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential
• Spectrum of the Schrödinger operator in a perturbed periodically twisted tube
• Homogenization of the Schrödinger equation and effective mass theorems
• Schrödinger operator. Estimates for number of bound states as function-theoretical problem
• Stability of the Magnetic Schrödinger Operator in a Waveguide
• On the curvature and torsion effects in one dimensional waveguides

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