Aharonov-Bohm ring touching a quantum wire: how to model it and to solve the inverse problem

DOI10.1016/S0034-4877(12)60010-XzbMath1250.81038OpenAlexW2154089068MaRDI QIDQ442064

Magnus Enerbäck, Pavel Kurasov

Publication date: 9 August 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(12)60010-x

zbMATH Keywords

inverse problemsquantum graphs

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse scattering problems in quantum theory (81U40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Quantum waveguides, quantum wires (82D77)

Related Items (6)

A Calderón type inverse problem for tree graphs ⋮ On vertex conditions for elastic systems ⋮ Visibility of quantum graph spectrum from the vertices ⋮ Inverse scattering for lasso graph ⋮ Incompleteness of resonance states for quantum ring with two semi-infinite edges ⋮ Schrödinger operators on graphs and geometry. II: Spectral estimates for \(L_1\)-potentials and an Ambartsumian theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inverse problems for quantum trees. II: Recovering matching conditions for star graphs
• Linear representations and isospectrality with boundary conditions
• On recovering Sturm-Liouville operators on graphs
• Inverse problems for quantum trees
• An inverse problem for Sturm-Liouville differential operators on A-graphs
• Scattering problems on noncompact graphs
• Symmetries of quantum graphs and the inverse scattering problem
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• Kirchhoff's Rule for Quantum Wires. II: The Inverse Problem with Possible Applications to Quantum Computers
• Can one hear the shape of a graph?
• Can one distinguish quantum trees from the boundary?
• Inverse spectral problems for differential operators on arbitrary compact graphs
• Geometric properties of quantum graphs and vertex scattering matrices
• Scattering from isospectral quantum graphs
• Boundary spectral inverse problem on a class of graphs (trees) by the BC method
• Inverse problems for Aharonov–Bohm rings
• Inverse problems for Sturm-Liouville operators on graphs with a cycle
• The isospectral fruits of representation theory: quantum graphs and drums
• Inverse problems for Sturm–Liouville operators on bush-type graphs
• On the inverse scattering problem on branching graphs
• Inverse problems for differential operators on trees with general matching conditions
• A Borg–Levinson theorem for trees
• Quantum graphs: I. Some basic structures
• Inverse spectral problems for Sturm–Liouville operators on graphs
• Inverse spectral problem for quantum graphs
• Inverse problems on graphs: recovering the tree of strings by the BC-method
• Recovering Sturm-Liouville operators from spectra on a graph with a cycle

This page was built for publication: Aharonov-Bohm ring touching a quantum wire: how to model it and to solve the inverse problem