近日，美国新墨西哥大学的Pablo M. Pogg课题组成功地在算子分布的长时间特性中获得了置乱和量子混沌指示器。相关研究成果已于2023年3月21日在国际权威学术期刊《物理评论A》上发表。

该课题组通过在完整的基础上展开目标算符来分析算符置乱，并研究了在算符空间中作为粗粒度概率分布处理的展开系数的结构。他们研究了这种分布的不同特征，比如它的均值、方差和参与率，分别应用于具有纵向和横向场的Ising模型、脉冲集体自旋模型和随机电路模型。研究表明，在这些情况下，算符分布的长时间性质具有共同特征，并讨论了如何将这些性质用作量子混沌的指示器。最后，他们还讨论了与OTOC（非时序关联）的联系，并分析了使用这些关联函数探测算符分布的实验成本。

据介绍，置乱是量子多体系统非平衡性质分析的关键概念。大多数研究都关注通过OTOC函数来表征其性质，特别是通过OTOC的早期衰减。然而，置乱是一个涉及算符扩散和算符纠缠的复杂过程，一个全面的表征需要访问多个时间尺度上的算符动力学的更精细信息。

附：英文原文

Title: Scrambling and quantum chaos indicators from long-time properties of operator distributions

Author: Sivaprasad Omanakuttan, Karthik Chinni, Philip Daniel Blocher, Pablo M. Poggi

Issue&Volume: 2023/03/21

Abstract: Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation (OTOC) functions, particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.

DOI: 10.1103/PhysRevA.107.032418

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.032418