On the Pauli operator for the Aharonov-Bohm effect with two solenoids
Mathematical Physics
2015-06-26 v1 math.MP
Spectral Theory
Abstract
We consider a spin-1/2 charged particle in the plane under the influence of two idealized Aharonov-Bohm fluxes. We show that the Pauli operator as a differential operator is defined by appropriate boundary conditions at the two vortices. Further we explicitly construct a basis in the deficiency subspaces of the symmetric operator obtained by restricting the domain to functions with supports separated from the vortices. This construction makes it possible to apply the Krein's formula to the Pauli operator.
Keywords
Cite
@article{arxiv.math-ph/0310029,
title = {On the Pauli operator for the Aharonov-Bohm effect with two solenoids},
author = {V. A. Geyler and P. Stovicek},
journal= {arXiv preprint arXiv:math-ph/0310029},
year = {2015}
}
Comments
LaTeX source file with 3 figures, to appear in JMP