不相交子系统的量子复杂性动力学
Quantum Complexity Dynamics for Disjoint Subsystems
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中文总结 AI 辅助
该研究结合全息学与随机量子电路，揭示非连通子系统的量子复杂性演化存在独特热效应与时间尺度缩放规律，深化了几何与计算复杂性的对应关系。
中文摘要 AI 辅助
量子复杂性已成为探测混沌、热化以及局域可观测量达到平衡后长时间尺度上黑洞内部的自然探针。然而，其时间演化几乎仅在局限于单个连通区域的子系统中被研究。我们利用全息学和随机量子电路的互补工具表明，由多个不相交区域构成的非连通子系统会产生与连通情况相比性质全新的物理现象。首先，在有限温度下，占据总系统不到一半的子系统在后期可携带高复杂性，而其更大补体的复杂性仍保持较低。这种通常层级的反转本质上是热的：它在无限温度极限（即随机量子电路所模拟的 regime）中消失。其次，若子系统的复杂性在早期达到平衡，将其拆分为m个不相交分量可将该时间尺度进一步降低m倍，我们在全息学和随机量子电路中均展示了这一现象。这些结果不仅加深了几何与计算复杂性概念之间的对应关系，还推动了对量子动力学中新型复杂性现象的探索。
英文摘要
Quantum complexity has emerged as a natural probe of chaos, thermalization, and the black hole interior on timescales long after local observables have equilibrated. However, its time evolution has been studied almost exclusively in subsystems confined to a single connected region. We show, using complementary tools from holography and random quantum circuits, that noncontiguous subsystems composed of multiple disjoint regions give rise to qualitatively new physics compared to the contiguous case. First, at finite temperature, a subsystem occupying less than half of the total system can carry high complexity at late times, even as the complexity of its larger complement remains low. This inversion of the usual hierarchy is intrinsically thermal: it vanishes in the infinite-temperature limit, which is the regime modeled by random quantum circuits. Second, if a subsystem's complexity equilibrates at an early time, then fragmenting it into $m$ disjoint components can further reduce this timescale by a factor of $m$, a phenomenon we exhibit in both holography and random quantum circuits. These results not only sharpen the correspondence between geometric and computational notions of complexity, but also motivate the search for novel complexity phenomena in quantum dynamics.
