Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves

Igor L. Aleiner, Lara Faoro, Lev B. Ioffe

Research output: Contribution to journalArticlepeer-review

118 Scopus citations

Abstract

We extend the Keldysh technique to enable the computation of out-of-time order correlators such as 〈O(t)Õ(0)O(t)Õ(0)〉. We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics. Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.

Original languageEnglish (US)
Pages (from-to)378-406
Number of pages29
JournalAnnals of Physics
Volume375
DOIs
StatePublished - Dec 1 2016

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • Decoherence
  • Out-of-time order
  • Quantum butterfly

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