We study the Lyapunov exponent ${\lambda }_L$ in quantum field theories with spacetime-independent disorder interactions. Generically ${\lambda }_L$ can only be computed at isolated points in parameter space, and little is known about the way in which chaos grows as we deform the theory away from weak coupling. In this paper, we describe 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 surprising behaviors in some cases, including a discontinuous transition into chaos. We also derive self-consistency equations for the two- and four-point functions for products of $N$ nontrivial conformal field theories deformed by disorder at leading order in $1/N$.

中文翻译：

---

无序 CFT 中量子混沌的开始

我们研究李雅普诺夫指数${\lambda }_{\mathrm{大号}}$在具有时空无关无序相互作用的量子场论中。一般${\lambda }_{\mathrm{大号}}$只能在参数空间中的孤立点处计算，并且对于我们将理论从弱耦合中变形时混沌增长的方式知之甚少。在本文中，我们描述了无序耦合是完全边缘变形的理论家族，使我们能够遵循${\lambda }_{\mathrm{大号}}$从弱耦合到强耦合。我们在某些情况下发现了令人惊讶的行为，包括不连续地过渡到混乱。我们还推导出二点和四点函数乘积的自洽方程$ñ$非平凡共形场理论在领先的秩序中被无序变形$1/ñ$.