Spectral asymptotics for waveguides with perturbed periodic twisting

DOI10.4171/JST/126zbMath1337.35105arXiv1407.0757OpenAlexW2964244482MaRDI QIDQ290731

Georgi D. Raikov

Publication date: 3 June 2016

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0757

zbMATH Keywords

eigenvalue asymptoticswaveguidesspectral gapsFloquet-Bloch theorySchrödinger operators with decaying oscillating potentials

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 (4)

Eigenvalue counting function for Robin Laplacians on conical domains ⋮ Lifshits tails for randomly twisted quantum waveguides ⋮ Lifshitz tails for quantum waveguides with random boundary conditions ⋮ Discrete spectrum for Schrödinger operators with oscillating decaying potentials

Cites Work

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• Gap opening and split band edges in waveguides coupled by a periodic system of small windows
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Corrections to the classical behavior of the number of bound states of Schrödinger operators
• Comparison theorems for the gap of Schrödinger operators
• Band gap of the spectrum in periodically curved quantum waveguides
• Absolute continuity in periodic thin tubes and strongly coupled leaky wires
• Endpoints of the spectrum of periodic operators are generically simple.
• Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials
• On the absolutely continuous spectrum of multi-dimensional Schrödinger operators with slowly decaying potentials
• Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS

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