论文标题
非线性矢量力学中的经典和量子蝴蝶效应
Classical and quantum butterfly effect in nonlinear vector mechanics
论文作者
论文摘要
我们在非线性矢量力学中使用$ O（n）$对称性的非线性矢量力学中的经典和量子蝴蝶效应之间建立了对应关系。一方面，我们分析使用增强的Schwinger-keldysh技术，以较大的限制来计算计算超时有序相关功能和量子Lyapunov指数。另一方面，我们从数字上估计经典混乱行为的高温极限中的经典lyapunov指数。在这两种情况下，Lyapunov的指数大约重合和比例为$κ\约1.3 \ sqrt [4] {λt}/n $与温度$ t $，自由度$ n $的数量，并耦合常数$λ$。
We establish the correspondence between the classical and quantum butterfly effects in nonlinear vector mechanics with the broken $O(N)$ symmetry. On one hand, we analytically calculate the out-of-time ordered correlation functions and the quantum Lyapunov exponent using the augmented Schwinger-Keldysh technique in the large-$N$ limit. On the other hand, we numerically estimate the classical Lyapunov exponent in the high-temperature limit, where the classical chaotic behavior emerges. In both cases, Lyapunov exponents approximately coincide and scale as $κ\approx 1.3 \sqrt[4]{λT}/N$ with temperature $T$, number of degrees of freedom $N$, and coupling constant $λ$.
