Dissipative Nonlinear Dynamics in Holography

TL;DR

This paper investigates nonlinear scalar field dynamics in AdS black brane backgrounds, revealing chaotic behavior and bifurcations, with implications for strongly coupled systems via holography.

Contribution

It demonstrates the emergence of chaos and bifurcations in holographic nonlinear dynamics, linking black hole physics to chaotic systems and quench phenomena.

Findings

Transition to chaos via period-doubling bifurcations.

Dissipation naturally arises from horizon conditions.

Holographic dual exhibits chaotic operator response.

Abstract

We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.