Quadratic forms for Aharonov-Bohm Hamiltonians

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 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 Aharonov-Bohm flux parameter goes to zero is discussed in terms of $\Gamma$ - convergence.

21 pages, contribution to the proceedings of the intensive period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, March-May 2022 (see https://sites.google.com/view/iqm22)

References in corpus (3)

• Mathematical justification of the Aharonov-Bohm hamiltonian
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Gauge invariance of the local phase in the Aharonov-Bohm interference: quantum electrodynamic approach

Cited by in corpus (3)

• Pauli Hamiltonians with an Aharonov-Bohm Flux
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Deficiency indices for singular magnetic Schrödinger operators