Speaker: Sriram Ganeshan

Simons Center, Stony Brook University

Title: Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

Abstract:

One of the central goals in the study of quantum chaos is to establish a correspondence principle between classical chaos and quantum dynamics. Due to the singular nature of the \hbar→ 0 limit, it has been a long-standing problem to recover key fingerprints of classical chaos such as the Lyapunov exponent starting from a microscopic quantum calculation. It was recently proposed that the out-of-time-ordered four-point correlator (OTOC) might serve as a useful characteristic of quantum-chaotic behavior because, in the semi-classical limit, its rate of exponential growth resembles the classical Lyapunov exponent. In this talk, I will present OTOC as a tool to unify the classical, quantum chaotic and weak localization regime for the quantum kicked rotor model–a textbook model of quantum chaos. Through OTOC, I will demonstrate how chaos develops in the quantum chaotic regime and is subsequently destroyed by the quantum interference effects that result in dynamical localization. We also make a quantitative comparison between the growth rate of OTOC and the classical Lyapunov exponent. Time permitting, I will introduce an integrable version of a linear rotor model with interactions that serve as a solvable model for many body localization in Floquet systems.