Classical and quantum butterfly effect in nonlinear vector mechanics

• URL: http://arxiv.org/abs/2205.05663v2
• Date: Sat, 25 Jun 2022 21:10:35 GMT
• Title: Classical and quantum butterfly effect in nonlinear vector mechanics
• Authors: Nikita Kolganov, Dmitrii A. Trunin
• Abstract summary: We establish the correspondence between the classical and quantum butterfly effects in nonlinear vector mechanics. We numerically estimate the classical Lyapunov exponent in the high-temperature limit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\kappa \approx 1.3 \sqrt[4]{\lambda T}/N$ with temperature $T$, number of degrees of freedom $N$, and coupling constant $\lambda$.

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