Out-of-time-ordered correlators in Bose-Hubbard systems

Out-of-time-ordered correlators (OTOCs) are quantum objects that can be used as a probe for quantum chaos. They characterise information scrambling, more specifically how a local operator commute with another initially local but time-evolved operator, and are studied here in the context of Bose-Hubbard systems. We derived a classical limit using and the van Vleck-Gutzwiller propagator. For short times, we are able to recover the Wigner-Moyal result, i.e. a Poisson bracket leading to an exponential growth in time. In addition, we are able to derive a classical finite long-time (i.e., saturation) value of the OTOC, provided that the accessible region of the phase space is bounded.