临界状态下的信息压缩
Information Compression at Criticality
浏览论文内容
中文总结 AI 辅助
研究遍历性临界边界处高激发量子态动力学性质，通过能量空间固有信息压缩揭示其复杂性，利用截断哈密顿量谱简化描述动力学，证明少量本征能级可重现生存概率幂律衰减，截断谱有分形结构。
中文摘要 AI 辅助
已知在遍历性临界边界处的高激发量子态偏离热行为，但其动力学性质仍知之甚少。在此，我们通过能量空间中固有信息压缩的视角揭示临界状态下量子动力学的复杂性。我们表明哈密顿量谱可被系统地截断，在保留其基本特征的同时简化动力学描述。具体而言，对于相互作用和非相互作用系统，我们证明哈密顿量本征能级的消失部分足以重现生存概率的幂律衰减。所得截断谱呈现分形结构，其特征为具有幂律尾部的值距分布，而其谱形状因子与生存概率表现出相同的渐近幂律衰减。
英文摘要
Highly excited quantum states at the critical boundary of ergodicity are known to deviate from thermal behavior, yet their dynamical properties remain poorly understood. Here, we uncover the complexity of quantum dynamics at criticality through the lens of intrinsic information compression in energy space. We show that the Hamiltonian spectrum can be systematically truncated, yielding a simplified description of the dynamics while preserving its essential features. Specifically, for both interacting and noninteracting systems, we demonstrate that a vanishing fraction of Hamiltonian eigenlevels suffices to reproduce the power-law decay of the survival probability. The resulting truncated spectrum exhibits a fractal structure characterized by a level-spacing distribution with a power-law tail, while its spectral form factor displays the same asymptotic power-law decay as the survival probability.
