Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes

DOI10.1134/S000143460905006XzbMath1181.35150OpenAlexW2051914736MaRDI QIDQ1033977

V. V. Grushin

Publication date: 10 November 2009

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s000143460905006x

zbMATH Keywords

Schrödinger operatorDirichlet conditionquantum waveguideFrenet equationsMaslov canonical operatoreigenvalues of the Laplace operatorthin infinite tube

Mathematics Subject Classification ID

Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (6)

The emergence of eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin strip ⋮ Magnetic effects in curved quantum waveguides ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes ⋮ Asymptotic behavior of the eigenvalues of the Schrödinger operator in thin closed tubes ⋮ Planar waveguide with “twisted” boundary conditions: Small width

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bound states in a locally deformed waveguide: The critical case
• Quantum and classical dynamics of an electron in thin curved tubes with spin and external electromagnetic fields taken into account
• Asymptotic solutions of nonrelativistic equations of quantum mechanics in curved nanotubes. I: Reduction to spatially one-dimensional equations
• Mathematical aspects of integral optics.
• On the eigenvalues of finitely perturbed Laplace operators in infinite cylindrical domains
• Asymptotic behavior of the eigenvalues of the Schrödinger operator with transversal potential in a weakly curved infinite cylinder
• Geometrically induced discrete spectrum in curved tubes
• Bound states in curved quantum waveguides
• A quantum pipette
• Weakly coupled bound states in quantum waveguides
• Bound states in quantum waveguides of a slowly decaying curvature
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
• ON A CLASS OF ELLIPTIC PSEUDODIFFERENTIAL OPERATORS DEGENERATE ON A SUBMANIFOLD
• Bound states in weakly deformed strips and layers.

This page was built for publication: Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes