随机幺正动力学下的平移对称性恢复
Translation symmetry restoration under random unitary dynamics
AI总结：
本文研究随机幺正电路中的平移对称性恢复，证明其时间尺度正比于子系统体积，并在中等子系统中首次精确刻画了量子姆潘巴效应。
摘要：
一个大的、局域相互作用的非平衡制备多体系统的有限部分最终会达到平衡。然而，刻画这一过程的潜在机制及其时间尺度尤为困难，因为这需要将普适特征与依赖于具体可观测量的特征解耦。近期，通过研究动力学中某些被初态破坏的对称性如何在给定子系统的约化态层面上恢复，获得了新的认识。这提供了一种高层次的、不依赖于可观测量的探针。迄今为止，这一思想已被应用于内部对称性的恢复，例如与电荷守恒相关的U(1)对称性。在此我们证明，同样的逻辑可以应用于时空对称性的恢复，因此可用于刻画完全一般系统的弛豫。我们通过考虑“通用”多体动力学的典型例子，即局域随机幺正电路，来说明这一思想，在该系统中我们的方法可得到精确结果。我们证明，在这些系统中平移对称性的恢复仅发生在正比于子系统体积的时间尺度上。事实上，对于足够大的子系统，对称性恢复时间变得与初态无关（只要后者在零时刻破坏该对称性），并与热化时间一致。然而，对于中等大小的子系统，可以观察到所谓的“量子姆潘巴效应”，即系统初态越不对称，其恢复对称性的速度反而越快。我们首次给出了这一效应在不可积系统中的精确刻画。
英文摘要：
The finite parts of a large, locally interacting many-body system prepared out-of-equilibrium eventually equilibrate. Characterising the underlying mechanisms of this process and its timescales, however, is particularly hard as it requires to decouple universal features from observable-specific ones. Recently, new insight came by studying how certain symmetries of the dynamics that are broken by the initial state are restored at the level of the reduced state of a given subsystem. This provides a high level, observable-independent probe. Until now this idea has been applied to the restoration of internal symmetries, e.g. U(1) symmetries related to charge conservation. Here we show that that the same logic can be applied to the restoration of space-time symmetries, and hence can be used to characterise the relaxation of fully generic systems. We illustrate this idea by considering the paradigmatic example of "generic" many-body dynamics, i.e. a local random unitary circuit, where our method leads to exact results. We show that the restoration of translation symmetry in these systems only happens on time-scales proportional to the subsystem's volume. In fact, for large enough subsystems the time of symmetry restoration becomes initial-state independent (as long as the latter breaks the symmetry at time zero) and coincides with the thermalisation time. For intermediate subsystems, however, one can observe the so-called "quantum Mpemba effect", where the state of the system restores a symmetry faster if it is initially more asymmetric. We provide the first exact characterisation of this effect in a non-integrable system.
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