Diffraction of the Aharonov–Bohm Hamiltonian

Yang, Mengxuan

doi:10.1007/s00023-021-01069-6

Cited by 4 publications

(1 citation statement)

References 29 publications

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“…These single-flux Hamiltonians include the Friedrichs realization and a 4-parameter family of singular perturbations thereof, describing s-wave and p-wave zero-range interactions. The spectral and scattering properties of these operators were further investigated in [PR11,Ru83,Ta99,Y21]. General results on the scattering matrix and total cross section for Schrödinger operators related to the single flux Friedrichs Hamiltonian were derived in [RY02,Ya03,Ya06] by means of stationary representation formulas and pseudo-differential methods.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Magnetic perturbations of anyonic and Aharonov–Bohm Schrödinger operators

Correggi

Fermi

2021

Journal of Mathematical Physics

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We study the Hamiltonian describing two anyons moving in a plane in the presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schrödinger operator. We also discuss the associated model describing a quantum particle immersed in a magnetic field with a local Aharonov–Bohm singularity. For a special class of magnetic potentials, we provide a complete classification of all possible self-adjoint extensions.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Magnetic perturbations of anyonic and Aharonov–Bohm Schrödinger operators

Correggi

Fermi

2021

Journal of Mathematical Physics

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Schrödinger Operators with Multiple Aharonov–Bohm Fluxes

Correggi,

Fermi

2024

Ann. Henri Poincaré

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We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of $$ N \geqslant 1$$ N ⩾ 1 Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.

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Resolvent Estimates for the Magnetic Hamiltonian with Singular Vector Potentials and Applications

Yang

2022

Commun. Math. Phys.

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Diffraction of the Aharonov–Bohm Hamiltonian

Cited by 4 publications

References 29 publications

Magnetic perturbations of anyonic and Aharonov–Bohm Schrödinger operators

Magnetic perturbations of anyonic and Aharonov–Bohm Schrödinger operators

Schrödinger Operators with Multiple Aharonov–Bohm Fluxes

Resolvent Estimates for the Magnetic Hamiltonian with Singular Vector Potentials and Applications

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