Emergent time crystals from phase-space noncommutative quantum mechanics

• URL: http://arxiv.org/abs/2207.00346v1
• Date: Fri, 1 Jul 2022 11:24:26 GMT
• Title: Emergent time crystals from phase-space noncommutative quantum mechanics
• Authors: Alex E. Bernardini and Orfeu Bertolami
• Abstract summary: We show that noncommutativity drives the amplitude of periodic oscillations identified as time crystals. A natural extension of our analysis shows how the spontaneous formation of time quasi-crystals can arise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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