横场伊辛链中印记相位噪声下动态冻结态的拉伸指数熔化
Stretched-Exponential Melting of a Dynamically Frozen State Under Imprinted Phase Noise in the Ising Chain in a Transverse Field
AI总结：
本文研究横场伊辛链中动态冻结态在印记相位噪声下的稳定性，发现该冻结态以拉伸指数方式缓慢熔化而非指数衰减，揭示了强周期驱动下涌现守恒量对随机相位扰动的鲁棒性特征。
摘要：
动态冻结是一种现象，在封闭量子系统中，一组局域可观测量在强周期驱动下涌现为近似但稳定的守恒量（冻结）。这些涌现守恒量的期望值在其各自初始值附近表现出小幅波动。这些波动不随时间增长，并且其幅度可以通过调节驱动参数被急剧调低。在这项工作中，我们探究了动态冻结对随机扰动的鲁棒性，这些随机扰动被添加到每个驱动周期后时间演化波函数中干涉态（自然基的元素）之间的相对相位上。我们在时间周期横场中的可积伊辛链中研究了这一问题。我们的关键发现是，印记的相位噪声熔化了动态冻结态，但衰减是“缓慢的”：是拉伸指数衰减而非指数衰减。拉伸指数衰减（也称为Kohlrausch弛豫）通常出现在具有时间尺度层级的复杂系统中，这些层级由强无序或其他导致堵塞、玻璃化或局域化的不均匀性引起。
英文摘要：
Dynamical freezing is a phenomenon where a set of local observables emerges as approximate but stable conserved quantities (freezes) under a strong periodic drive in a closed quantum system. The expectation values of these emergent conserved quantities exhibit small fluctuations around their respective initial values. These fluctuations do not grow with time, and their magnitude can be tuned down sharply by tuning the drive parameters. In this work, we probe the resilience of dynamical freezing to random perturbations added to the relative phases between the interfering states (elements of a natural basis) in the time-evolving wave function after each drive cycle. We study this in an integrable Ising chain in a time-periodic transverse field. Our key finding is, that the imprinted phase noise melts the dynamically frozen state, but the decay is "slow": a stretched-exponential decay rather than an exponential one. Stretched-exponential decays (also known as Kohlrausch relaxation) are usually expected in complex systems with time-scale hierarchies due to strong disorders or other inhomogeneities resulting in jamming, glassiness, or localization.
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