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arXiv · 2207.00346

Emergent time crystals from phase-space noncommutative quantum mechanics

Alex E. Bernardini·Orfeu Bertolami
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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.

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Alex E. Bernardini, Orfeu Bertolami. 2022-07-01. Emergent time crystals from phase-space noncommutative quantum mechanics. https://doi.org/10.1016/j.physletb.2022.137549

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