Dynamical confinement for Schrödinger operators with magnetic potential and Aharonov–Bohm effect

DOI10.1063/5.0159003OpenAlexW4390780742MaRDI QIDQ6188545

Renan G. Romano, César R. de Oliveira

Publication date: 7 February 2024

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

Full work available at URL: https://doi.org/10.1063/5.0159003

Mathematics Subject Classification ID

Atomic physics (81V45) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Cites Work

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• On confining potentials and essential self-adjointness for Schrödinger operators on bounded domains in \(\mathbb R^n\)
• Impenetrability of Aharonov-Bohm solenoids: proof of norm resolvent convergence
• Self-adjoint, globally defined Hamiltonian operators for systems with boundaries
• High-velocity estimates for the scattering operator and Aharonov-Bohm effect in three dimensions
• Superconductivity and the Aharonov-Bohm effect
• Confining quantum particles with a purely magnetic field
• The Aharonov-Bohm effect and scattering theory
• Effet d'Aharonov-Bohm sur un état borné de l'équation de Schrödinger. (Aharonov-Bohm effect for a bounded state of the Schrödinger equation)
• Mathematical justification of the Aharonov-Bohm Hamiltonian
• Nodal sets for ground states of Schrödinger operators with zero magnetic field in non simply connected domains
• On the Aharonov-Bohm Hamiltonian
• Elliptic partial differential equations of second order
• A new version of the Aharonov-Bohm effect
• The role of idealizations in the Aharonov-Bohm effect
• Idealizations, essential self-adjointness, and minimal model explanation in the Aharonov-Bohm effect
• Eigenvalues upper bounds for the magnetic Schrödinger operator
• A global, dynamical formulation of quantum confined systems
• Significance of Electromagnetic Potentials in the Quantum Theory
• Distributions and Operators
• Self-adjoint extensions of restrictions
• Aharonov–Bohm effect with δ-type interaction
• On the mathematical theory of the Aharonov$ndash$Bohm effect
• Aharonov-Bohm effect without contact with the solenoid
• Differential Forms in Electromagnetics
• Can elementary quantum mechanics explain the Aharonov–Bohm effect?
• Scattering and self-adjoint extensions of the Aharonov–Bohm Hamiltonian
• All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations
• The Refractive Index in Electron Optics and the Principles of Dynamics