标题： 改进对开放量子系统中算子大小动力学的理解 显示英文标题

标题： Refining the Understanding of Operator Size Dynamics in Open Quantum Systems

摘要： 信息混淆是指在多体系统中，局部量子信息在单位演化下在整个系统中分散的现象。 它在封闭量子系统中已被广泛研究，其中通过算子大小增长来量化，揭示了凝聚态物理、高能物理和量子信息之间的深刻联系。 然而，当将算子大小动力学的研究扩展到开放量子系统时，会出现两种不同的算子大小分布定义。 这些定义基于对环境的不同处理方式。 在这项工作中，我们旨在建立开放量子系统中算子大小动力学的统一图景，使用可解的布朗运动SYK模型在一般系统尺寸下进行研究。 特别是，我们提供了在使用一种特定定义发现的混淆转变特征，在另一种定义下的算子大小动力学中出现的条件。 此外，我们通过探索之前研究未捕捉到的有限尺寸效应，扩展了先前的研究。 我们的结果为开放量子系统中的算子大小动力学提供了更深入的理解。 显示英文摘要

摘要： Information scrambling refers to the phenomenon in which local quantum information in a many-body system becomes dispersed throughout the entire system under unitary evolution. It has been extensively studied in closed quantum systems, where it is quantified by operator size growth, revealing deep connections between condensed matter physics, high-energy physics, and quantum information. However, when extending the study of operator size dynamics to open quantum systems, two different definitions of operator size distributions emerge. These definitions are based on different treatments of the bath. In this work, we aim to establish a unified picture for operator size dynamics in open quantum systems, using the solvable Brownian SYK models at generic system size. In particular, we provide the conditions under which the signature of scrambling transition, discovered using one particular definition, appears in operator size dynamics under the other definition. Additionally, we extend previous studies by exploring finite-size effects that are not captured by the scramblon theory. Our results provide a refined understanding of operator size dynamics in open quantum systems.