标题： Krylov指数和最大量子混沌的功率谱：一种有效场论方法 显示英文标题

标题： Krylov exponents and power spectra for maximal quantum chaos: an EFT approach

摘要： 我们通过Krylov复杂性和通用算符增长假说的视角来研究最大混沌的有效场论（EFT）。 我们检验了量子混沌的两种度量之间的关系：时间有序相关函数（OTOCs）和Krylov复杂性。 在EFT中，流体力学模式的平移对称性在OTOCs中强制最大李雅普诺夫指数，$\lambda_L = 2\pi T$，同时限制热力学两点自相关函数。 我们求解了自相关函数上的这些约束，并计算了几种示例的Lanczos系数和Krylov指数，发现两者分别为$\lambda_K = \lambda_L$和$\lambda_K = \lambda_L/2$。 这表明，在EFT中，仅靠平移对称性不足以强制最大Krylov指数，即使李雅普诺夫指数已经是最大的。 特别是，这一结果与猜想的界限$\lambda_L \leq \lambda_K \leq 2\pi T$存在矛盾。 最后，我们找到了自相关函数的解，其功率谱非常类似于全息系统中所谓的热力学乘积公式。 显示英文摘要

摘要： We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators (OTOCs) and Krylov complexity. In the EFT, a shift symmetry of the hydrodynamic modes enforces the maximal Lyapunov exponent in OTOCs, $\lambda_L = 2\pi T$, while simultaneously constraining thermal two-point autocorrelators. We solve these constraints on the autocorrelator, and calculate the Lanczos coefficients and Krylov exponents for several examples, finding both $\lambda_K = \lambda_L$ and $\lambda_K = \lambda_L/2$. This demonstrates that, within the EFT, the shift symmetry alone is insufficient to enforce maximal Krylov exponents even when the Lyapunov exponent is maximal. In particular, this result suggests a tension with the conjectured bound $\lambda_L \leq \lambda_K \leq 2\pi T$. Finally, we identify autocorrelator solutions whose power spectra closely resemble the so-called thermal product formula seen in holographic systems.