自旋构型动力学在幺正演化与周期性投影测量下的复杂性
Complexity of spin configurations dynamics due to unitary evolution and periodic projective measurements
AI总结：
该研究通过主成分分析量化多体量子系统在周期性投影测量下的自旋构型动力学复杂性，发现PCA复杂性随时间快速增长后趋于平台，并指出局域动力学与测量方向可预测其参数敏感性。
摘要：
我们研究了一个多体量子系统在周期性投影测量下的哈密顿动力学，该系统导致概率性元胞自动机动力学。给定一系列测量值，我们通过主成分分析来表征其动力学。我们研究了所需主成分的数量，即我们称之为PCA复杂性的复杂度度量，作为哈密顿参数和测量间隔的函数。我们考虑了描述相互作用、非相互作用、可积和不可积系统的不同哈密顿量，包括随机局域哈密顿量和平移不变随机局域哈密顿量。在所有情况下，我们发现PCA复杂性随时间快速增长，然后接近平台期。PCA复杂性的动力学可以随哈密顿参数和测量协议在定量和定性上变化。重要的是，对于缺乏简单局域动力学的模型（如非可积模型中常见的情况），PCA复杂性的动力学对特定系统参数的敏感性显著降低。特别地，我们指出一个考虑局域动力学和测量方向的品质因数，以预测PCA复杂性动力学对系统参数的敏感性。
英文摘要：
We study the Hamiltonian dynamics of a many-body quantum system subjected to periodic projective measurements which leads to probabilistic cellular automata dynamics. Given a sequence of measured values, we characterize their dynamics by performing a principal component analysis. The number of principal components required for an almost complete description of the system, which is a measure of complexity we refer to as PCA complexity, is studied as a function of the Hamiltonian parameters and measurement intervals. We consider different Hamiltonians that describe interacting, non-interacting, integrable, and non-integrable systems, including random local Hamiltonians and translational invariant random local Hamiltonians. In all these scenarios, we find that the PCA complexity grows rapidly in time before approaching a plateau. The dynamics of the PCA complexity can vary quantitatively and qualitatively as a function of the Hamiltonian parameters and measurement protocol. Importantly, the dynamics of PCA complexity present behavior that is considerably less sensitive to the specific system parameters for models which lack simple local dynamics, as is often the case in non-integrable models. In particular, we point out a figure of merit that considers the local dynamics and the measurement direction to predict the sensitivity of the PCA complexity dynamics to the system parameters.
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