While a clean, driven system generically absorbs energy until it reaches “infinite temperature,” it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for nontrivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localized cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al. [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.

中文翻译：

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没有温度的预热

尽管清洁的驱动系统通常会吸收能量直到其达到“无限温度”，但它可能会非常缓慢地表现出所谓的预热状态。在这里，我们表明，在周期性驱动的（Floquet）系统中出现了一个额外的近似守恒的量，可以产生一个类似的长寿命制度。相对于控制预热动力学的有效哈密顿量，这甚至可以允许非平凡的动力学，即使是处于高温或无限温度的初始状态。我们介绍了具有这种预热状态的具体设置，其中一种具有周期加倍（时间晶体）响应。我们还提出了一种直接诊断方法，以将这种预热现象与其无限长寿命的多体局部表亲区分开来。我们将这些见解应用于Rovny最近进行的NMR实验的模型中等。[物理 牧师 120，180603（2018）]，其，有趣的是，检测到的时间的Floquet晶体的签名在一个干净的三维材料。我们表明，其驱动协议的轻微但微妙的变化可以将时晶信号的寿命增加几个数量级。