Chaos in Bose-Hubbard systems: Lyapunov exponents, Ehrenfest time, and scrambling

We study one-dimensional Bose-Hubbard systems,
or chains, which are describing many-body ultra-
cold bosonic atoms. Our goal is to study quantum chaos in such systems, and see if it can be linked to classical chaos by considering the (semi)classical equivalent of the system. In addition to purely quantum time-evolution simulations, the numerical tools used for this purpose are a mean-field Gross-Pitaevskii description of the system and a truncated Wigner (tW) approach. We will see if signatures of chaos can be found in out-of-time-ordered correlators (OTOCs), and how it can be linked to the deviation of classical trajectories.