Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems

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.