Quadratic forms for Aharonov-Bohm Hamiltonians

• URL: http://arxiv.org/abs/2208.06285v1
• Date: Fri, 12 Aug 2022 14:13:07 GMT
• Title: Quadratic forms for Aharonov-Bohm Hamiltonians
• Abstract summary: Quadratic form techniques are used to characterize different self-adjoint realizations of the reduced two-dimensional Schr"odinger operator. The limit of the singularity of the Friedrichs Hamiltonian when the Aharonov-Bohm flux parameter goes to zero is discussed in terms of $Gamma$ - convergence.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a charged quantum particle immersed in an axial magnetic field, comprising a local Aharonov-Bohm singularity and a regular perturbation. Quadratic form techniques are used to characterize different self-adjoint realizations of the reduced two-dimensional Schr\"odinger operator, including the Friedrichs Hamiltonian and a family of singular perturbations indexed by $2 \times 2$ Hermitian matrices. The limit of the Friedrichs Hamiltonian when the Aharonov-Bohm flux parameter goes to zero is discussed in terms of $\Gamma$ - convergence.

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