NEWS: The CQM Distinguished Lecture series has been established  in the Fall of 2015 to bring to Stony Brook University the renown experts in the physics of quantum matter.

The lectures in this series will attract a broad audience of physicists from SBU and BNL,
and SBU graduate students.
@ Solid State Seminar
Oct 20 @ 1:30 pm – 2:30 pm

Speaker: Sriram Ganeshan

Simons Center, Stony Brook University

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


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.