The Quantum-Butterfly effect from a kinetic equation approach

We here study chaos in many-body quantum systems. We follow a recently developed approach which builds on kinetic equations for generalized distributions. These distributions store information on so-called out-of time ordered correlation functions, which can show an exponential increase in time, the quantum butterfly effect. The latter is currently widely used as a diagnostic tool for many-body chaos, and within the kinetic approach the quantum butterfly effect manifests in an instability related to positive eigenvalues of the relevant collision integrals. The latter determine the Lyapunov rates on which many-body chaos establishes. We here derive the generalized kinetic equations using an augmented Keldysh technique. We then apply the method to study many-body chaos in a weakly interacting electron gas, and derive the Lyapunov exponent for this system.