# Induction of chaotic fluctuations in particle dynamics in a uniformly accelerated frame

## TL;DR

This study demonstrates that a horizon in a uniformly accelerated frame can induce chaotic behavior in a particle trapped in a harmonic oscillator, independent of intrinsic curvature or gravity effects.

## Contribution

It provides a model showing that horizons alone can cause chaos in particle dynamics, supporting the conjecture that horizons induce chaos without gravitational curvature.

## Key findings

- Horizon presence can induce chaos in particle motion.
- Chaotic behavior depends on parameters like acceleration and energy.
- System transitions from periodic to chaotic states.

## Abstract

The ongoing conjecture that the presence of horizon may induce chaos in an integrable system, is further investigated from the perspective of a uniformly accelerated frame. Particularly, we build up a model which consists of a particle (massless and chargeless) trapped in harmonic oscillator in a uniformly accelerated frame (namely Rindler observer). Here the Rindler frame provides a Killing horizon without any intrinsic curvature to the system. This makes the present observations different from previous studies. We observe that for some particular values of parameters of the system (like acceleration, energy of the particle), the motion of the particle trapped in harmonic potential systematically goes from periodic state to the chaotic. This indicates that the existence of horizon alone, not the intrinsic curvature (i.e. the gravitational effect) in the background, is sufficient to induce the chaotic motion in the particle. We believe the present study further enlighten and balustrade the conjecture.