论文标题
量子混乱和状态传播的复杂性
Quantum chaos and the complexity of spread of states
论文作者
论文摘要
我们提出了一种量子状态复杂性的度量，通过最大程度地减少波功能在所有基础上的扩散。我们的措施受到状态保持不变的“生存振幅”的控制，并且可以在具有离散光谱的理论中有效计算。对于连续的哈密顿进化，它将Krylov操作员的复杂性推广到量子状态。我们将方法应用于谐波和倒置的振荡器，群歧管上的粒子，Schwarzian理论，SYK模型和随机矩阵模型。对于混沌系统中的随时间发展的热菲尔德双状态，我们的措施显示了四个机制：直至熵中指数级的“峰”的线性“斜坡”，然后是“坡度”下降到“高原”。这些机制出现在相同的物理学中，产生光谱形式的斜率 - 斜坡 - 斑点结构。具体而言，复杂性斜率由光谱刚度引起，从而区分了不同的随机矩阵集合。
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently computed in theories with discrete spectra. For continuous Hamiltonian evolution, it generalizes Krylov operator complexity to quantum states. We apply our methods to the harmonic and inverted oscillators, particles on group manifolds, the Schwarzian theory, the SYK model, and random matrix models. For time-evolved thermofield double states in chaotic systems our measure shows four regimes: a linear "ramp" up to a "peak" that is exponential in the entropy, followed by a "slope" down to a "plateau". These regimes arise in the same physics producing the slope-dip-ramp-plateau structure of the Spectral Form Factor. Specifically, the complexity slope arises from spectral rigidity, distinguishing different random matrix ensembles.
