Strong chaos, the butterfly effect, is a ubiquitous phenomenon in physical systems. In quantum mechanical systems, one of the diagnostics of quantum chaos is an out-of-time-order correlation function, related to the commutator of operators separated in time. In this talk we will review the work of Maldacena, Shenker and Stanford (arxiv:1503.01409), who conjectured that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λL ≤ 2πkBT/\hbar. We will then discuss a system that displays a maximal Lyapunov exponent: the SYK model.
