We study the quantum Lyapunov exponent ${\lambda }_L$ in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of $N$ models coupled by disorder at large $N$, generalizing the equations appearing in SYK-like models. We then study families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow ${\lambda }_L$ from weak to strong coupling. We find interesting behaviors, including a discontinuous transition into chaos, mimicking classical KAM theory.

中文翻译：

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随机场理论中量子混沌的开始

我们研究量子李雅普诺夫指数${\lambda }_{\mathrm{大号}}$在具有时空无关无序的理论中。我们首先推导出二点和四点函数的自洽方程$ñ$模型被大体上的无序耦合$ñ$，概括出现在类似 SYK 的模型中的方程。然后，我们研究无序耦合是完全边际变形的理论家族，使我们能够遵循${\lambda }_{\mathrm{大号}}$从弱耦合到强耦合。我们发现有趣的行为，包括不连续过渡到混沌，模仿经典的 KAM 理论。