Scattering, spectrum and resonance states completeness for a quantum graph with Rashba Hamiltonian

DOI10.1007/978-3-030-51945-2_4zbMath1472.81251OpenAlexW3141666603MaRDI QIDQ1980906

Irina V. Blinova, Maria O. Smolkina, Igor Yu. Popov

Publication date: 9 September 2021

Full work available at URL: https://doi.org/10.1007/978-3-030-51945-2_4

zbMATH Keywords

spectrumcompletenessresonancespin-orbit interaction

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) (S)-matrix theory, etc. in quantum theory (81U20) Applications of functional analysis in quantum physics (46N50) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Resonances in quantum scattering theory (81U24)

Cites Work

• Quantum dot with attached wires: resonant states completeness
• On the resonances of the Laplacian on waveguides
• Incompleteness of resonance states for quantum ring with two semi-infinite edges
• Harmonic analysis of operators on Hilbert space
• On resonances and bound states of Smilansky Hamiltonian
• Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction
• Complex resonances in acoustic waveguides
• Completeness of resonance states for quantum graph with two semi-infinite edges
• Open quantum dots: Resonances from perturbed symmetry and bound states in strong magnetic fields
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