Many-body interference, chaos and operator spreading in interacting quantum systems
Concepts based on multi-particle interference have proven very fruitful for better understanding various many-body phenomena, including scattering in photonic networks, quantum dynamics of cold atoms, many-body localization and more recently information scrambling. With regard to the latter, so-called out-of-time-order correlators (OTOCs) presently receive particular attention as sensitive probes for chaos and the temporal growth of complexity in interacting systems. We will address such phenomena using semiclassical path intergral techniques based on interfering Feynman paths, bridging classical and quantum many-body approaches. This enables us to compute OTOCs and related observables non-perturbatively in terms of coherent sums over interfering solutions of the corresponding classical mean-field equations, thereby including entanglement and correlation effects. Moreover, on the numerical side we devise a semiclassical method for large-N Bose-Hubbard systems far-out-of equilibrium that allows us to calculate many-body quantum interference in Fock space on time scales far beyond the so-called crambling Ehrenfest time.