Non-Markovian environment induced chaos in optomechanical system

TL;DR

This paper demonstrates that chaos in an optomechanical system can be entirely induced by non-Markovian environmental effects, independent of traditional non-linear interactions or external forces.

Contribution

It reveals that non-Markovian environment-induced memory effects alone can generate chaos, providing a new perspective on chaotic dynamics in quantum systems.

Findings

Chaos arises solely from non-Markovian effects, not optomechanical coupling.

Non-Markovian corrections induce non-linearity through time-domain convolutions.

Chaos disappears under Markovian conditions where these convolutions become constants.

Abstract

In traditional research, chaos is frequently accompanied by non-linearity, which typically stems from non-linear interactions or external driving forces. However, in this paper, we present the chaotic behavior that is completely attributed to the non-linear back-reaction of non-Markovian environment. To be specific, we derive the dynamical equations of an optomechanical system and demonstrate that the non-linearity (cause of chaos) in the equations arises entirely from the time-domain convolutions (TDCs) induced by non-Markovian corrections. Under Markovian conditions, these TDCs are reduced into constants, thereby losing the nonlinearity and ultimately leading to the disappearance of chaos. Furthermore, we also observe chaos generation in the absence of optomechanical couplings, which further confirms that the non-Markovian effect is the sole inducement of chaos and the environmental parameters play important roles in the generation of chaos. We hope these results may open a new direction to investigate chaotic dynamics purely caused by non-Markovian environments.