Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

TL;DR

This paper explores how noncommutative quantum mechanics modifies the Aharonov-Bohm and related effects, providing new limits on noncommutative parameters and analyzing experimental implications.

Contribution

It derives the phase in noncommutative space for the Spavieri effect and sets a significantly improved experimental limit on the noncommutative parameter.

Findings

Improved the limit on noncommutative parameter by 10 orders of magnitude.

Found that noncommutative phases of Aharonov-Casher and He-McKellar-Willkens effects are nullified in current experiments.

Provided theoretical analysis of quantum effects in noncommutative space.

Abstract

Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-bohm effect which involving a coherent superposition of particles with opposite charges moving along single open interferometric path. By means of the experimental considerations a limit $\sqrt{\theta}\simeq\left( 0,13T\text{eV}\right) ^{-1}$ is achieved, improving by 10 orders of magnitude the derived by Chaichian et. al. for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.