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arXiv 2006.01227cond-mat.stat-mechquant-ph
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开放量子系统中的经典亚稳态理论

Theory of classical metastability in open quantum systems

Katarzyna Macieszczak, Dominic C. Rose, Igor Lesanovsky, Juan P. Garrahan

备注：
28 pages (89 pages with Supplemental Material), 7 figures
发表信息：
Phys. Rev. Research 3, 033047 (2021)
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摘要：

本文提出了开放量子系统中经典亚稳态的一般理论。亚稳态是动力学中时间尺度的大分离的结果，导致系统状态出现静止状态时存在一种状态，然后在更大的时间内最终松弛到真正的静止状态。在这项工作中，我们专注于经典亚稳态的出现，即，当具有时间尺度分离的开放量子系统的亚稳态可以近似为有限数量的状态的概率混合时。我们发现，一些经典的功能遵循这种近似，为流形的亚稳态，它们之间的长时间动态，和对称性的动态。也就是说，这些状态近似不相交，从而发挥亚稳相的作用，向稳态的弛豫近似由它们之间的经典随机动力学，弱对称性对应于它们的排列。重要的是，经典动力学不仅在平均水平上观察到，而且在单个量子轨迹的水平上观察到：我们表明，时间粗粒度的连续测量记录可以被视为噪声经典轨迹，而它们的统计数据可以近似为经典动力学的统计数据。其中，这解释了一阶动力学相变是如何从亚稳态中产生的。最后，为了验证在一个给定的开放量子系统的经典亚稳性的存在下，我们开发了一个有效的数值方法，提供了一套亚稳相连同有效的经典动力学。由于接近一阶耗散相变表现为亚稳性，在这项工作中引入的理论和工具可以用来调查这样的过渡，通过亚稳行为的多体系统的中等大小的数字访问。

英文摘要：

We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear stationary, before eventual relaxation toward a true stationary state at much larger times. In this work, we focus on the emergence of classical metastability, i.e., when metastable states of an open quantum system with separation of timescales can be approximated as probabilistic mixtures of a finite number of states. We find that a number of classical features follow from this approximation, for the manifold of metastable states, long-time dynamics between them, and symmetries of the dynamics. Namely, those states are approximately disjoint and thus play the role of metastable phases, the relaxation toward the stationary state is approximated by a classical stochastic dynamics between them, and weak symmetries correspond to their permutations. Importantly, the classical dynamics is observed not only on average, but also at the level of individual quantum trajectories: We show that time coarse-grained continuous measurement records can be viewed as noisy classical trajectories, while their statistics can be approximated by that of the classical dynamics. Among others, this explains how first-order dynamical phase transitions arise from metastability. Finally, to verify the presence of classical metastability in a given open quantum system, we develop an efficient numerical approach that delivers the set of metastable phases together with the effective classical dynamics. Since the proximity to a first-order dissipative phase transition manifests as metastability, the theory and tools introduced in this work can be used to investigate such transitions through the metastable behavior of many-body systems of moderate sizes accessible to numerics.

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