Emergent time crystals from phase-space noncommutative quantum mechanics

TL;DR

This paper demonstrates that phase-space noncommutativity in quantum mechanics can lead to emergent time crystal behavior, including periodic oscillations and quasi-crystals, without requiring spontaneous symmetry breaking.

Contribution

It introduces a novel connection between phase-space noncommutativity and the emergence of time crystals in quantum systems.

Findings

Noncommutativity induces periodic oscillations in quantum harmonic oscillators.

Phase-space noncommutativity can lead to the spontaneous formation of time quasi-crystals.

The analysis uses the Weyl-Wigner-Groenewold-Moyal framework to support predictions.

Abstract

It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our point is that such effects do emerge from position ($\hat{q}_i$) and/or momentum ($\hat{p}_i$) noncommutativity, i.e., from $[\hat{q}_i,\,\hat{q}_j]\neq 0$ and/or $[\hat{p}_i,\,\hat{p}_j]\neq 0$ (for $i\neq j$). In such a context, a predictive analysis is carried out for the $2$-dim noncommutative quantum harmonic oscillator through a procedure supported by the Weyl-Wigner-Groenewold-Moyal framework. This allows for the understanding of how the phase-space noncommutativity drives the amplitude of periodic oscillations identified as time crystals. A natural extension of our analysis also shows how the spontaneous formation of time quasi-crystals can arise.