Diffraction of the Aharonov-Bohm Hamiltonian

Abstract

In this paper, we compute the diffractive wave propagator of the Aharonov-Bohm effect on ${\mathbf{R}}^2$ with a single solenoid using a technique of moving solenoid location. In addition, we compute the corresponding diffraction coefficient which is the principal symbol of the diffractive propagator. This paper gives the first proof of propagation of singularities of the Aharonov-Bohm Hamiltonian.

This is a pre-published version. The published version is available at https://rdcu.be/clTMj

References in corpus (4)

• On Schroedinger operators with inverse square potentials on the half-line
• Mathematical justification of the Aharonov-Bohm hamiltonian
• On radial Schroedinger operators with a Coulomb potential
• Magnetic Perturbations of Anyonic and Aharonov-Bohm Schrödinger Operators

Cited by in corpus (2)

• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications