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Area of Science:

  • Quantum chaos
  • Holographic principle
  • Statistical mechanics

Background:

  • Holographic theories with classical gravity duals exhibit maximal chaos, saturating the universal bound on chaos growth.
  • It remains an open question whether this maximal chaos is exclusive to leading large N correlators or extends to other systems.

Purpose of the Study:

  • To investigate if maximal chaos, a property of holographic theories, can manifest in simpler systems.
  • To explore the behavior of chaos in a probe sector without explicit gravitational degrees of freedom.

Main Methods:

  • Analysis of a Brownian particle coupled to a thermal ensemble.
  • Calculation of the four-point out-of-time-order correlator (OTOC) to diagnose chaos.
  • Comparison of the Lyapunov exponent and scrambling time with established holographic models.

Main Results:

  • The four-point OTOC in the Brownian particle system exhibits an initial exponential growth rate that saturates the chaos bound (Lyapunov exponent λL=2π/β).
  • The scrambling time (t* ~ βlog(sqrt[λ])) is found to be parametrically smaller than in plasma excitations (t* ~ βlogN^2).

Conclusions:

  • Maximal chaos can be achieved in simpler probe sectors, such as a Brownian particle in a thermal ensemble.
  • This finding suggests that explicit gravitational degrees of freedom are not always necessary to attain maximal chaos.