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arXiv · 2208.06285

Quadratic forms for Aharonov-Bohm Hamiltonians

Davide Fermi
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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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Davide Fermi. 2022-08-12. Quadratic forms for Aharonov-Bohm Hamiltonians. https://doi.org/10.1007/978-981-99-5894-8_7

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