Dynamics of scrambling of information, from shock waves to Fisher-KPP

Information scrambling is the mechanism by which localized information in an extended system flows to non-local degrees of freedom, becoming practically irretrievable. It proceeds via two mechanisms, namely a rapid loss and a spatial spreading of information, which can sometimes be associated with the concepts of Lyapunov exponent and butterfly velocity, respectively.

In this presentation, I will provide a partial overview of the field of quantum chaos and discuss our current understanding of the phenomenon of scrambling in thermalizing systems. I will explain how conventional tools of quantum transport theory can be adapted to derive a large-scale effective kinetic theory of scrambling. More specifically, I will focus on the case of realistic metals that experience both inelastic scattering due to interactions and elastic scattering due to disorder. I will demonstrate that disorder drives a phase transition in the scrambling dynamics, from shock-wave dynamics to dynamics belonging to the Fisher or Kolmogorov–Petrovsky–Piskunov class. More generally, this approach can be used to gain insight into the mysterious relationship between transport properties and chaos.