论文标题
SU（2）Yang-Mills理论的运营商增长
Operator growth in SU(2) Yang-Mills theory
论文作者
论文摘要
Krylov的复杂性是一种可观察到的新颖的，用于检测量子混乱，也是可能的重力双重的指标。在本文中，我们计算了SU（2）Yang-Mills理论中的Krylov复杂性和相关的Lanczos系数，该理论可以简化为非线性耦合的谐波振荡器（CHO）模型。我们表明，Krylov复杂性的生长中存在混乱的过渡。 Krylov的复杂性在早期阶段显示出二次生长，然后线性增长。相应的Lanczos系数满足了通用算子生长假设，即首先生长，然后进入饱和平台。通过兰开斯系数的线性生长，我们获得了量子Lyapunov指数的上限。最后，我们研究了不同能量部门对K-复合性和兰开斯系数的影响。
Krylov complexity is a novel observable for detecting quantum chaos, and an indicator of a possible gravity dual. In this paper, we compute the Krylov complexity and the associated Lanczos coefficients in the SU(2) Yang-Mills theory, which can be reduced to a nonlinearly coupled harmonic oscillators (CHO) model. We show that there exists a chaotic transition in the growth of Krylov complexity. The Krylov complexity shows a quadratic growth in the early time stage and then grows linearly. The corresponding Lanczos coefficient satisfies the universal operator growth hypothesis, i.e., grows linearly first and then enters the saturation plateau. By the linear growth of Lanczos coefficients, we obtain an upper bound of the quantum Lyapunov exponent. Finally, we investigate the effect of different energy sectors on the K-complexity and Lanczos coefficients.
