Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators

Understand

Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in interacting quantum systems.

• They exhibit a characteristic classical exponential growth, but saturate beyond the so-called scrambling or Ehrenfest time $\tau_{\rm E}$ in the quantum correlated regime.
• Here we present a path-integral approach for the entire time evolution of OTOCs for bosonic $N$-particle systems.
• We first show how the growth of OTOCs up to $\tau_{\rm E} = (1/\lambda) \log N$ is related to the Lyapunov exponent $\lambda$ of the corresponding chaotic mean-field dynamics in the semiclassical large-$N$ limit.