Gap asymptotics in a weakly bent leaky quantum wire

DOI10.1088/1751-8113/48/49/495301zbMath1330.81101arXiv1506.07309OpenAlexW1895338395MaRDI QIDQ3462559

Sylwia Kondej, Pavel Exner

Publication date: 15 January 2016

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

Full work available at URL: https://arxiv.org/abs/1506.07309

zbMATH Keywords

asymptotic expansionweak perturbationsingular Schrödinger operatorsdelta interactionleaky quantum wires

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (7)

On the bound states of Schrödinger operators with δ-interactions on conical surfaces ⋮ Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions ⋮ Leaky quantum structures ⋮ Scattering of particles bounded to an infinite planar curve ⋮ Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane ⋮ Spectral properties of soft quantum waveguides ⋮ Bound states asymptotics in the system with quantum wires in ℝ³

Cites Work

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• Weakly coupled bound state of 2-D Schrödinger operator with potential-measure
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Schrödinger operators with singular interactions
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• Leaky Quantum Graphs: A Review
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Spectral asymptotics of a broken δ-interaction
• A Krein-like formula for singular perturbations of self-adjoint operators and applications

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