We investigate why the Lyapunov exponents λ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound λ<2πkBT/ℏ by probing imaginary-time path-integral space using ring-polymer molecular dynamics (RPMD) for a barrier-crossing model. We find that the RPMD OTOC satisfies the same bound as the quantum OTOC, which is caused by the stability of quantum thermal fluctuations around the instanton on the barrier. We expect that similar instantons (or other delocalised structures) will be found in many other systems with exponentially growing OTOCs.
@article{arxiv.2212.10202,
title = {Instantons and the quantum bound to chaos},
author = {Vijay Ganesh Sadhasivam and Lars Meuser and David R. Reichman and Stuart C. Althorpe},
journal= {arXiv preprint arXiv:2212.10202},
year = {2023}
}