An isoperimetric problem for leaky loops and related mean-chord inequalities

DOI10.1063/1.1914728zbMath1110.81076arXivmath-ph/0501066OpenAlexW3099813159MaRDI QIDQ3438448

Pavel Exner

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0501066

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (10)

Generalized Eigenfunctions and Spectral Theory for Strongly Local Dirichlet Forms ⋮ Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces ⋮ Essential spectrum of Schrödinger operators with \(\delta\)-interactions on unbounded hypersurfaces ⋮ Inequalities for means of chords, with application to isoperimetric problems ⋮ Spectral isoperimetric inequalities for singular interactions on open arcs ⋮ Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\) ⋮ On geometric perturbations of critical Schrödinger operators with a surface interaction ⋮ On the critical exponent in an isoperimetric inequality for chords ⋮ Optimization of the lowest eigenvalue for leaky star graphs ⋮ Essential spectrum of Schrödinger operators with 𝛿 and 𝛿^{′}-interactions on systems of unbounded smooth hypersurfaces in ℝⁿ

Cites Work

• Unnamed Item
• A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions
• Schrödinger operators with singular interactions
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Geometrically induced spectrum in curved leaky wires
• On the Placement of an Obstacle or a Well so as to Optimize the Fundamental Eigenvalue
• Leaky quantum graphs: approximations by point-interaction Hamiltonians

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