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“Quantum Lyapunov Exponents”

Date:

Download-files:

Time:

Thursday, 17. Jan. 2019

Video-Recording for any system with MP4-support

- Video.mp4 (ca.409 Mb)

15:15 – 16:25

Victor Galitski

(University of Maryland)

Abstract :

The hallmark of classical chaos is an exponential divergence of initially infinitesimally

close trajectories - a phenomenon colloquially known as the “butterfly effect.”

This exponential runaway of chaotic trajectories is quantitatively characterized by the

Lyapunov exponent. Of great interest has been to understand how/if the butterfly effect

and Lyapunov exponents generalize to quantum physics, where the notion of a trajectory

does not exist.

In this talk, I will discuss recent progress in resolving this fundamental challenge that is

based on a newly introduced measure of quantum chaoticity – the out-of-time-ordered

correlator or “Lyapunovian” – which enables to make a non-trivial connection between

classical and quantum chaos in a variety of systems: from single-particle chaotic billiards

to disordered condensed matter systems to models of black holes. I will illustrate the use

of the Lyapunovian on a few standard examples that will be used to elucidate the nature

of quantum chaotic dynamics, including suppression of the butterfly effect in quantum

systems. I will conclude by formulating an intriguing conjecture connecting quasiclassical

chaotic dynamics and statistics of energy levels in interacting many-body quantum systems.