Diffraction of the Aharonov-Bohm Hamiltonian

TL;DR

This paper analyzes the diffraction phenomena of the Aharonov-Bohm Hamiltonian on a plane with a solenoid, providing the first proof of singularity propagation and explicit diffraction coefficients.

Contribution

It introduces a novel technique of moving the solenoid to compute the diffractive wave propagator and proves propagation of singularities for the Aharonov-Bohm Hamiltonian.

Findings

Computed the diffractive wave propagator for the Aharonov-Bohm effect.

Derived the diffraction coefficient as the principal symbol.

Provided the first proof of propagation of singularities for this 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.