Schr\"{o}dinger operators with multiple Aharonov-Bohm fluxes

TL;DR

This paper analyzes the Schr"{o}dinger operator for a 2D quantum particle with multiple Aharonov-Bohm fluxes, classifying all self-adjoint realizations and studying their spectral and scattering properties.

Contribution

It provides a complete classification of self-adjoint realizations of the Schr"{o}dinger operator with multiple Aharonov-Bohm fluxes and investigates their spectral and scattering behavior.

Findings

Explicit characterization of self-adjoint domains and actions.

Proof of existence and completeness of wave operators.

Analysis of spectral and scattering properties.

Abstract

We study the Schr\"{o}dinger operator describing a two-dimensional quantum particle moving in presence of $ N \geqslant 1 $ Aharonov-Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.