The operator L\'evy flight: light cones in chaotic long-range interacting systems

TL;DR

This paper explores how chaotic systems with power-law interactions exhibit emergent light cone structures that limit information spread, depending on interaction decay and system dimension, with a novel Le9vy flight interpretation.

Contribution

It introduces a framework linking chaos, long-range interactions, and emergent light cones, including a Le9vy flight perspective and numerical validation in 1D spin models.

Findings

Linear light cone for a9 d+1/2 interactions

Le9vy flight interpretation of information propagation

Numerical evidence from 1D long-range spin models

Abstract

We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension $d$ and the exponent $\alpha$ governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for $\alpha \ge d+1/2$. We also provide a L\'evy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1d long-range spin models with 200 sites.