论文标题
来自相位非交通量子力学的新兴时间晶体
Emergent time crystals from phase-space noncommutative quantum mechanics
论文作者
论文摘要
有人认为，时间晶体的存在需要对连续的时间翻译对称性的自发分解，以说明量子可观察到基态的意外非平稳行为。我们的观点是，这种效果确实从位置（$ \ hat {q} _i $）和/或动量（$ \ hat {p} _i $）non -Commutativity，即，从$ [\ hat {q} _i，\ hat {q} _i，\，\，\，\，\ hat {q} _j} _j] \ neq和/或/或/或/或/或/或/或/或/或/或$ [\ hat {p} _i，\，\ hat {p} _j] \ neq 0 $（对于$ i \ neq j $）。在这种情况下，通过Weyl-Wigner-Groenewold-Moyal-Moyal框架支持的过程，对$ 2 $ -DIM非交通量子谐波振荡器进行了预测分析。这允许理解相位非交构性如何驱动确定为时间晶体的周期性振荡的幅度。我们的分析的自然扩展还表明了时间的自发形成准晶体。
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.
