Emergent time crystals from phase-space noncommutative quantum mechanics
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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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Cited by 3 Pith papers
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Spin-Induced Fractal Time-Crystal-Like Dynamics and Non-Markovian Memory in the Bateman Dual Oscillator
Spin-induced noncommutativity in the Bateman oscillator yields discrete scaling covariance in amplified and damped modes, producing self-similar evolution and history-dependent non-Markovian reduced dynamics.
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Spin-Induced Non-Markovian Time-Crystal-Like Dynamics and Fractal Scaling in the Bateman Dual Oscillator
Spin-induced deformation in the Bateman dual oscillator framework yields non-Markovian reduced dynamics with persistent oscillations and fractal scaling that mimic time crystals in a globally unitary quantum system.
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Spin-Induced Non-Markovian Time-Crystal-Like Dynamics and Fractal Scaling in the Bateman Dual Oscillator
Spin-induced deformation creates a Bateman dual oscillator whose reduced non-Markovian dynamics produces time-crystal-like ordering and fractal scaling in a closed quantum system.
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