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                                         “Quantum Lyapunov Exponents”





 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.


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