English

Does scrambling equal chaos?

Statistical Mechanics 2020-04-09 v2 Disordered Systems and Neural Networks High Energy Physics - Theory Chaotic Dynamics

Abstract

Focusing on semiclassical systems, we show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model. We derive a lower bound on the OTOC Lyapunov exponent which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e. for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos.

Keywords

Cite

@article{arxiv.1912.11063,
  title  = {Does scrambling equal chaos?},
  author = {Tianrui Xu and Thomas Scaffidi and Xiangyu Cao},
  journal= {arXiv preprint arXiv:1912.11063},
  year   = {2020}
}

Comments

6 pages, 5 figures; v2: accepted version

R2 v1 2026-06-23T12:55:05.248Z