Noncommutative analogue Aharonov-Bohm effect and superresonance

TL;DR

This paper models a rotating acoustic black hole using a noncommutative spacetime framework, analyzing superresonance and the Aharonov-Bohm effect, revealing persistent phase shifts and their competition in this setting.

Contribution

It introduces a noncommutative geometric approach to acoustic black holes, showing how noncommutativity affects superresonance and the Aharonov-Bohm effect.

Findings

Modified Aharonov-Bohm phase shift persists even when circulation and draining vanish.

Noncommutativity causes superresonance and AB effect to compete.

Spacetime noncommutativity influences wave scattering in acoustic black hole analogs.

Abstract

We consider the idea of modeling a rotating acoustic black hole by an idealized draining bathtub vortex which is a planar circulating flow phenomenon with a sink at the origin. We find the acoustic metric for this phenomenon from a noncommutative Abelian Higgs model. As such the acoustic metric not only describes a rotating acoustic black hole but also inherits the noncommutative characteristic of the spacetime. We address the issues of superresonance and analogue Aharonov-Bohm (AB) effect in this background. We mainly show that the scattering of planar waves by a draining bathtub vortex leads to a modified AB effect and due to spacetime noncommutativity, the phase shift persists even in the limit where the parameters associated with the circulation and draining vanish. Finally, we also find that the analogue AB effect and superresonance are competing phenomena at a noncommutative spacetime.