Southwest Quantum Information and Technology

Generalizing the OTOC to yield Lyapunov exponents in the classical limit

Presenting Author: Charlie Kapsiak, Carleton College
Contributing Author(s): Alex Kiral, Arjendu Pattanayak

The out-of-time-ordered correlator is OTOC is used as a tool to diagnose quantum chaos. When applied to the position and time operators, it yields the Lyapunov exponent in the classical limit but only for the one-dimensional case or for a uniformly hyperbolic map such as the Cat Map. We construct the correct generalization to higher dimensional canonical phase spaces by demonstrating that a matrix of OTOCs yields the Jacobian of the dynamics in the classical limit and hence is able to recover the correct classical maximal Lyapunov exponent. We also construct the correct generalization for OTOCs for dynamics governed by Lie Algebras. We discuss the behavior of these generalized measures.

(Session 5 : Sunday from 5:00pm - 7:00pm)