Chaos, complexity, and random matrices

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us…

• NS
  National Science Foundation

  Award: 1125565
• UD
  U.S. Department of Energy
• GA
  Gordon and Betty Moore Foundation

  Awards: PHY-1125565, GBMF-2644
• GO
  Government of Canada
• IC
  Industry Canada
• IP
  Institut Périmètre de physique théorique
• OO
  Office of Science

  Award: DE-SC0011632
• IF
  Institute for Quantum Information and Matter, California Institute of Technology

  Award: PHY-1125565
• HE
  High Energy Physics

  Award: DE-SC0011632