论文标题
分析性约束结合光谱形式的衰减
Analyticity constraints bound the decay of the spectral form factor
论文作者
论文摘要
对于热平衡系统的系统，量子混乱不能快于$λ\ leq2π/（\hbarβ）$ [Maldacena，Shenker＆Stanford，Jhep（2016）]。 Lyapunov指数$λ$上的此“ MSS绑定”是由正规化的超级阶外相关器分析的条带的宽度设置的。我们表明，相似的约束也结合了光谱构造（SFF）的衰减，该谱尺寸（SFF）测量光谱相关性，并根据两级相关函数的傅立叶变换来定义。具体而言，我们引入的拐点指数$η$是表征SFF的早期衰减的，被限制为$η\leqπ/（2 \hbarβ）$。这种界限是普遍的，并且存在于混乱的政权之外。结果在具有规则，混乱和可调动力学的系统中说明，即单粒子谐波振荡器，许多粒子Calogero-Sutherland模型，随机矩阵理论的合奏，量子踢了顶部。讨论了与其他已知边界（包括量子速度限制）结合的派生界限的关系。
Quantum chaos cannot develop faster than $λ\leq 2 π/(\hbar β)$ for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent $λ$ is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponent $η$, that we introduce to characterize the early-time decay of the SFF, is bounded as $η\leq π/(2\hbarβ)$. This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
