When things stop falling, chaos is suppressed

TL;DR

This paper explores how the growth of operators in chaotic systems relates to particle dynamics in AdS black holes, showing that charge influences chaos suppression, supported by holographic models and examples.

Contribution

It provides a detailed analysis of operator growth and chaos suppression in charged black hole backgrounds, extending Susskind's proposal.

Findings

Charge affects particle momentum and operator size behavior.

Chaos suppression occurs at finite chemical potential.

Holographic models support the theoretical predictions.

Abstract

This note is devoted to the investigation of Susskind's proposal(arXiv:1802.01198) concerning the correspondence between the operator growth in chaotic theories and the radial momenta of the particle falling in the AdS black hole. We study this proposal and consider the simple example of an operator with the global charge described by the charged particle falling to the Reissner-Nordstrom-AdS black hole. Different charges of the particle lead to qualitatively different behavior of the particle momenta and consequently change of the operator size behavior. This holographic result is supported by different examples of chaotic models at a finite chemical potential where the suppression of chaos has been observed.