标题： 量子蜕变：可编程的涌现与多尺度系统中体-边二分法的瓦解 显示英文标题

标题： Quantum Metamorphosis: Programmable Emergence and the Breakdown of Bulk-Edge Dichotomy in Multiscale Systems

摘要： 多尺度协同作用——系统不同特征长度、时间和能量尺度之间的相互作用——正在成为许多当代科学分支中的统一线索。 从莫尔和超莫尔材料以及冷原子到DNA模板超晶格和嵌套光子网络，多尺度协同作用产生了在任何单一尺度上都无法获得的行为。 然而，缺乏一个能编程跨尺度相互作用以操控频谱、输运和拓扑的一般框架。 在此，我们将多尺度协同作用从副产品提升为新兴现象的通用设计原则。 具体而言，我们引入了一个可编程尺度的分层嵌套晶格（HNL）框架，该框架可以容纳量子形态变化（QuMorph）——一种由无量纲可调参数$α$（相对跃迁）控制的系统依赖特征的连续演化。 作为示例，我们展示了一个HNL，在其中随着$α$的变化，频谱从整数量子霍尔类似状态演变为异常量子霍尔类似状态，并经过一个具有大量小间隙的茧状区域。 这种多尺度混合产生了多种新现象，包括混合边缘-体态、尺度依赖拓扑、拓扑嵌入的平带以及孤立的边缘带。 我们提出了一种可行的光子实现方法，使用商用耦合谐振器阵列，概述了空间-频谱特征以映射QuMorph，并探索了多时间尺度非线性光学的应用。 我们的工作建立了一个可扩展和可编程的范式，用于工程多尺度的新兴现象。 显示英文摘要

摘要： Multiscale synergy -- the interplay of a system's distinct characteristic length, time, and energy scales -- is becoming a unifying thread across many contemporary branches of science. Ranging from moiré and super-moiré materials and cold atoms to DNA-templated superlattices and nested photonic networks, multiscale synergy produces behaviors not obtainable at any single scale alone. Yet a general framework that programs cross-scale interplay to steer spectra, transport, and topology has been missing. Here, we elevate multiscale synergy from a byproduct to a general design principle for emergent phenomena. Specifically, we introduce a scale-programmable framework for hierarchically nested lattices (HNLs) that can host quantum metamorphosis (QuMorph) -- a continuous evolution between system-dependent features governed by a dimensionless tunable parameter $α$ (the relative hopping). To exemplify, we show an HNL, in which as $α$ changes, the spectrum metamorphoses from integer quantum Hall-like to anomalous quantum Hall-like, passing through a cocoon regime with proliferating mini-gaps. This multiscale mixing yields multiple novel phenomena, including hybrid edge-bulk states, scale-dependent topology, topologically embedded flat bands, and isolated edge bands. We propose a feasible photonic implementation using commercially available coupled-resonator arrays, outline spatial-spectral signatures to map QuMorph, and explore applications for multi-timescale nonlinear optics. Our work establishes a scalable and programmable paradigm for engineering multiscale emergent phenomena.