On systems of maximal quantum chaos

A remarkable feature of chaos in many-body quantum systems is the existence a bound on Lyapunov exponent. An important question to understand what special about maximally chaotic which saturate this bound. Here we provide further evidence for `hydrodynamic' origin such systems, and discuss hallmarks systems. We first that hydrodynamic effective field theory previously proposed should be understood as then emphasize make explicit signature maximal was only implicit prior literature, namely suppression exponential growth commutator squares generic few-body operators. general argument within our theory, illustrate it using SYK models holographic speculate indicates nature operator scrambling fundamentally different non-maximally also simplest scenario regime at sufficiently large distances even