# Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry

## TL;DR

This paper investigates how noncommutative phase space properties influence persistent charged currents in metal rings, revealing that momentum noncommutativity causes observable asymmetries useful for experimental detection.

## Contribution

It introduces an asymmetry observable to measure momentum noncommutativity effects in persistent currents, highlighting a novel approach to probe noncommutative phase space.

## Key findings

- Coordinate noncommutativity affects current magnitude but is hard to observe.
- Momentum noncommutativity causes symmetry violation in the current.
- Asymmetry observable can detect momentum noncommutativity effects.

## Abstract

We study the physical properties of the persistent charged current in a metal ring on a noncommutative phase space, and temperature dependence of the noncommutative corrections are also analyzed. We find that the coordinate noncommutativity only affects the total magnitude of the current, and it is difficult to observe it. In contrast, the momentum noncommutativity can violate symmetry property of the current, and this violation of symmetry holds at a finite temperature. Based on this violation effect, we introduce an asymmetry observable to measure the momentum noncommutativity.