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Area of Science:

  • Complex Systems
  • Quantum Chaos
  • Statistical Physics

Background:

  • Chaotic systems with power-law interactions exhibit complex dynamics.
  • Information propagation in physical systems can be constrained by interaction ranges.
  • Quantum chaos provides a framework for understanding dephasing and stochastic processes.

Purpose of the Study:

  • To investigate emergent limits on information propagation in chaotic power-law interacting systems.
  • To establish an analogy between these limits and relativistic light cones.
  • To determine the dependence of these limits on spatial dimension and interaction decay exponent.

Main Methods:

  • Mapping the system to a stochastic model using the dephasing nature of quantum chaos.
  • Analyzing the phase diagram of the stochastic model.
  • Interpreting results through a Lévy flight (long-range random walk) model.
  • Conducting numerical simulations on 1D long-range spin models.

Main Results:

  • Emergent limits on information propagation analogous to relativistic light cones were identified.
  • A linear light cone emerges for spatial dimension d and exponent α satisfying α≥d+1/2.
  • The study provides a Lévy flight interpretation consistent with the findings.
  • Numerical data from 1D long-range spin models support the theoretical predictions.

Conclusions:

  • Chaotic power-law interacting systems possess fundamental limits on information propagation.
  • These limits are tunable by system dimensionality and interaction strength.
  • The findings offer insights into information dynamics in complex and quantum systems.