Quadratic forms for AharonovBohm Hamiltonians
Abstract
We consider a charged quantum particle immersed in an axial magnetic field, comprising a local AharonovBohm singularity and a regular perturbation. Quadratic form techniques are used to characterize different selfadjoint realizations of the reduced twodimensional Schrödinger 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 AharonovBohm flux parameter goes to zero is discussed in terms of $\Gamma$  convergence.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 DOI:
 10.48550/arXiv.2208.06285
 arXiv:
 arXiv:2208.06285
 Bibcode:
 2022arXiv220806285F
 Keywords:

 Mathematical Physics;
 Quantum Physics;
 47A07;
 49J45;
 81Q10
 EPrint:
 21 pages, contribution to the proceedings of the intensive period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, MarchMay 2022 (see https://sites.google.com/view/iqm22)