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Fine Grained Chaos in AdS_{2} Gravity.

Felix M Haehl1, Moshe Rozali1

  • 1Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada.

Physical Review Letters
|April 26, 2018
PubMed
Summary

Quantum chaos extends to higher-point functions, showing exponential growth in scrambling for quantum information. This reveals how complex quantum systems thermalize over time.

Area of Science:

  • Quantum physics
  • Chaos theory
  • Quantum information

Background:

  • Quantum chaos is often defined by the exponential growth of the thermal out-of-time-order four-point function.
  • This growth is limited by a characteristic scrambling time.

Purpose of the Study:

  • To generalize the characterization of quantum chaos to higher-point correlation functions.
  • To explore the dynamics of quantum information scrambling in specific theoretical models.

Main Methods:

  • Investigated the Schwarzian theory, which models two-dimensional anti-de Sitter space (AdS_{2}) gravity and Sachdev-Ye-Kitaev (SYK) model dynamics.
  • Identified and analyzed a specific class of 2k-point correlation functions termed "maximally braided" and "k-out of time order."

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Main Results:

  • These higher-point functions exhibit exponential growth up to extended scrambling times, scaling as u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}.
  • The study identified a set of 2k-point functions with this property.

Conclusions:

  • The findings suggest a generalized understanding of quantum chaos and thermalization in complex quantum systems.
  • This provides insights into the scrambling of quantum information, with finer-grained measures taking longer to thermalize.