More on chaos at weak coupling

Abstract

We discuss aspects of the quantum Lyapunov exponent $\hat{I}{»}_L$ in theories with an exactly marginal SYK-like random interaction, where $\hat{I}{»}_L$ can be computed as a continuous function of the interaction strength $\mathcal{J}$. In $1d$, we prove a conjecture from arXiv:2111.06108 which states that at small $\mathcal{J}$, $\hat{I}{»}_L$ can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the $2d$ version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.