Quasiclassical description of out-of-time-ordered correlators

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 local operator that is time-evolved. We present a quasiclassical formalism of OTOCs using the semiclassical van Vleck-Gutzwiller propagator in combination with the diagonal approximation. For short time, we recover the same result as with the Wigner-Moyal formalism, yielding an initial exponential growth of the correlator. For long times and fully chaotic dynamics, this quasiclassical formalism yields a finite saturation value of the OTOC. However, as we verified in Bose-Hubbard systems, this quasiclassical saturation value is found to be small compared to the actual quantum OTOC saturation threshold. This finding shows the importance of effects beyond quasiclassical physics related to trajectory pairs with small-angle crossings, as was pointed out in Ref. [1].

[1] 1.Rammensee, J., Urbina, J.-D. & Richter, K. Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators. Phys. Rev. Lett. 121, 124101 (2018).