Probing Out-of-Time-Order Correlators

In this talk I will present a method to probe the Out-of-Time-Order Correlators (OTOCs) of a general system by coupling it to a harmonic oscillator probe.  When the system's degrees of freedom are traced out, the OTOCs imprint themselves on the generalized influence functional of the oscillator. This generalized influence functional leads to a local effective action for the probe whose couplings encode OTOCs of the system. I will focus on the structural features of this effective action and the constraints on the couplings from microscopic unitarity. I will also discuss the additional constraints imposed on the effective couplings of the probe when the system is in a thermal state. Finally, I will describe a concrete model where all these analyses are applied to obtain an effective theory of the probe.