On the resonances and eigenvalues for a 1D half-crystal with localised impurity

DOI10.1515/CRELLE.2011.153zbMath1251.47066arXiv1107.2692MaRDI QIDQ3166326

Karl Michael Schmidt, Evgeny L. Korotyaev

Publication date: 11 October 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.2692

zbMATH Keywords

Schrödinger operatorperiodic potentialresonanceabsolutely continuous spectruminverse spectrumantibound state

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Statistical mechanics of crystals (82D25) Applications of operator theory in the physical sciences (47N50) Initial value problems for linear higher-order PDEs (35G10)

Related Items (12)

Schrödinger operators periodic in octants ⋮ Asymptotics of resonances for 1D Stark operators ⋮ Inverse resonance problem for Jacobi operators on a half-lattice ⋮ Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line ⋮ Resonances for Dirac operators on the half-line ⋮ Periodic Dirac operator with dislocation ⋮ Resonances of third order differential operators ⋮ Dubrovin equation for periodic Dirac operator on the half-line ⋮ Asymptotics of the \(S\)-matrix for perturbed Hill operators ⋮ Defect Resonances of Truncated Crystal Structures ⋮ Bound states for nano-tubes with a dislocation ⋮ Inverse resonance scattering on rotationally symmetric manifolds

Cites Work

• Symmetry of bound and antibound states in the semiclassical limit
• Gaps and bands of one dimensional periodic Schrödinger operators. II
• Distribution of poles for scattering on the real line
• Estimates of periodic potentials in terms of gap lengths
• Inverse problem and the trace formula for the Hill operator. II
• Asymptotic distribution of resonances in one dimension
• The inverse problem for the Hill operator. A direct approach
• Resonances in one dimension and Fredholm determinants
• Effective masses and conformal mappings
• Bounds on scattering poles in one dimension
• Resonances for steplike potentials: Forward and inverse results
• A Short Proof of Zheludev's Theorem
• A CHARACTERIZATION OF THE SPECTRUM OF HILL'S OPERATOR
• The inverse problem for periodic potentials
• ON THE INVERSE RESONANCE PROBLEM
• Inverse resonance scattering on the real line
• Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit
• The inverse resonance problem for perturbations of algebro-geometric potentials
• Symmetry of bound and antibound states in the semiclassical limit for a general class of potentials
• On the determination of a Hill's equation from its spectrum
• Unnamed Item
• Unnamed Item

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