Understanding the statistical origins of the quantum bound on chaos.

The process by which initially localized quantum information in a system is rendered irretrievable due to (usually chaotic) quantum dynamics, referred to as 'scrambling', has been a subject of intense interest in the last decade. The Out-of-time-ordered correlators (OTOCs) form an important class of quantitative tools that yield Lyapunov exponents which quantify the rate of scrambling in quantum systems. In thermal ensembles, these exponents are conjectured to obey a universal quantum bound (λ< 4π²kT/h, where k and h are the Boltzmann and Planck constants respectively). Our numerical investigation strongly suggests that, at least in quantum Boltzmann ensembles, the bound on λ is purely a quantum-statistical effect, which can be explained using imaginary-time Feynman path-integrals. Specifically, we find that delocalized structures in a fictitious extended phase space, that represents bounce instantons are responsible for this bound. This study has important ramifications about the nature of scrambling in quantum systems and demonstrates an important simulation paradigm for obtaining scrambling rates.