AI 中文总结
研究蒸发黑洞复杂度的页面转变，通过子系统复杂度的基 - 谱分解及CV提议，论证辐射复杂度有类似转变，且通过岛的出现解决了类似信息悖论的复杂度悖论。
AI 中文摘要
近期结果表明，对于哈尔随机态子系统，当分数子系统大小超过二分之一时，其复杂度存在类似佩奇的急剧转变。对于永恒反德西特黑洞边界子区域的全息复杂度，在假设子区域的复杂度等于体积（CV）提议时也会出现这种转变。我们将此转变解释为从谱主导到基主导的子系统复杂度的交叉，反映了超过半系统大小后近似热性质的失效。然后我们将此推理应用于与浴耦合的蒸发反德西特黑洞，其由在尺寸减小的内部子系统上进行随机演化的量子电路建模。利用子系统复杂度的基 - 谱分解，我们认为辐射复杂度中存在类似佩奇的转变。然后通过子区域的CV，我们表明通过一个岛的出现，相同的转变出现在辐射子系统的全息复杂度中，其体积给出主要贡献。我们认为岛体积贡献解决了类似于信息悖论的明显复杂度悖论。
英文摘要
Recent results demonstrate that there exists a sharp, Page-like transition for the complexity of subsystems of Haar-random states as their fractional subsystem size surpasses one half. They further demonstrate that this transition also occurs for the holographic complexity of boundary subregions of eternal AdS black holes, assuming the Complexity$=$Volume (CV) proposal for subregions. We interpret this transition as a crossover from spectrum-dominated to basis-dominated subsystem complexity, reflecting the breakdown of approximate thermality beyond half-system size. We then apply this reasoning to an evaporating AdS black hole coupled to a bath, modeled by a quantum circuit undergoing random evolution on an interior subsystem of diminishing size. Using the basis-spectrum decomposition of subsystem complexity, we argue for a similar Page-like transition in the radiation complexity. We then show, using CV for subregions, that the same transition appears in the holographic complexity of the radiation subsystem through the emergence of an island, whose volume gives the dominant contribution. We argue that the island volume contribution resolves an apparent complexity paradox analogous to the information paradox.
Comments32 pages, 6 figures
