A two-way approach to out-of-time-order correlators

Understand

Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos.

• Of the four operators involved, one pair may be regarded as a source and the other as a probe.
• A usual approach, applicable to large-$N$ systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour.
• We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time.