PIRSA:18100080

Quantum Lyapunov Exponents

Galitski, V. (2018). Quantum Lyapunov Exponents. Perimeter Institute. https://pirsa.org/18100080

Galitski, Victor. Quantum Lyapunov Exponents. Perimeter Institute, Oct. 04, 2018, https://pirsa.org/18100080 

          @misc{ pirsa_PIRSA:18100080,
            doi = {10.48660/18100080},
            url = {https://pirsa.org/18100080},
            author = {Galitski, Victor},
            keywords = {Condensed Matter, Other},
            language = {en},
            title = {Quantum Lyapunov Exponents},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {oct},
            note = {PIRSA:18100080 see, \url{https://pirsa.org}}
          }

Victor Galitski

University of Maryland, College Park

Talk number
PIRSA:18100080
Collection
Talk Type
Subject
Abstract

Classical chaotic systems exhibit exponential divergence of initially infinitesimally close trajectories, which is characterized by the Lyapunov exponent. This sensitivity to initial conditions is popularly known as the  "butterfly effect." Of great recent interest has been to understand how/if the butterfly effect and Lyapunov exponents generalize to quantum mechanics, where the notion of a trajectory does not exist. In this talk, I will introduce the measure of quantum chaoticity  – a so-called out-of-time-ordered four-point correlator (whose semiclassical limit reproduces classical Lyapunov growth), and use it to describe quantum chaotic dynamics and its eventual disappearance in the standard models of classical and quantum chaos – Bunimovich stadium billiard and standard map or kicked rotor [1]. I will describe our recent results on the quantum Lyapunov exponent in these single-particle models as well as results in interacting many-body systems, such as disordered metals [2]. The latter many-body model exhibits an interaction-induced transition from quantum chaotic to non-chaotic dynamics, which may manifest itself in a sharp change of the distribution of energy levels from Wigner-Dyson to Poisson statistics. I will conclude by formulating a many-body analogue of the Bohigas-Giannoni-Schmit conjecture.
References:
[1] "Lyapunov exponent and out-of-time-ordered correlator's growth rate in a chaotic system,"  E. Rozenbaum, S. Ganeshan, and V. Galitski, Physical Review Letters 118, 086801 (2017)
[2] "Non-linear sigma model approach to many-body quantum chaos," Y. Liao and and V. Galitski, arXiv:1807.09799