Existence of discrete eigenvalues for the Dirichlet Laplacian in a two-dimensional twisted strip

DOI10.1007/s00574-023-00339-7zbMath1515.81098arXiv2010.00034OpenAlexW3090531806MaRDI QIDQ6042640

Alessandra A. Verri, Rafael T. Amorim

Publication date: 3 May 2023

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.00034

zbMATH Keywords

discrete eigenvaluesDirichlet Laplaciantwisted stripsunbounded strips

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ruled strips with asymptotically diverging twisting
• On the spectrum of the Dirichlet Laplacian in a narrow strip
• On the spectrum of narrow periodic waveguides
• Perturbation theory for linear operators.
• Quantum strips on surfaces
• Existence of bound states in quantum waveguides under weak conditions
• Spectral asymptotics of the Dirichlet Laplacian in a conical layer
• Quantum waveguides
• Spectral analysis of sheared nanoribbons
• Spectrum of the Schrödinger operator in a perturbed periodically twisted tube
• Hardy inequalities in strips on ruled surfaces
• Geometrically induced discrete spectrum in curved tubes
• On the spectrum of curved planar waveguides
• Plane waveguides with corners in the small angle limit
• Quantum waveguides with corners
• Dirichlet Laplacian in a thin twisted strip
• THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS
• Location of the essential spectrum in curved quantum layers
• Quantum strips in higher dimensions
• Bound states in curved quantum waveguides
• Effective potentials of quantum strip waveguides and their dependence upon torsion
• Geometric coupling thresholds in a two-dimensional strip
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Bound states in weakly deformed strips and layers.
• Bound states in curved quantum layers

This page was built for publication: Existence of discrete eigenvalues for the Dirichlet Laplacian in a two-dimensional twisted strip