Probing Out-of-Time-Order Correlators

TL;DR

This paper introduces a method to measure out-of-time-order correlators (OTOCs) in a system by coupling it to a harmonic oscillator probe, allowing indirect probing through the probe's effective action.

Contribution

It develops a framework to extract OTOCs from a system via a harmonic oscillator probe and analyzes the resulting effective action and its constraints.

Findings

OTOCs are encoded in the influence functional of the probe

The effective action for the probe reveals the system's OTOCs

Constraints from microscopic unitarity on the couplings

Abstract

We 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. We study the structural features of this effective action and the constraints on the couplings from microscopic unitarity. We comment on how the OTOCs of the system appear in the OTOCs of the probe.