Entanglement of higher-derivative oscillators in holographic systems

TL;DR

This paper investigates quantum entanglement in higher-derivative Pais-Uhlenbeck oscillators within holographic systems, analyzing entanglement entropy, stability, and information geometry to deepen understanding of their quantum properties.

Contribution

It introduces a detailed analysis of entanglement entropy in coupled higher-derivative oscillators, linking thermodynamic parameters to quantum entanglement in holographic contexts.

Findings

Entanglement entropy depends on temperature, frequencies, and coupling parameters.

Higher-derivative oscillators exhibit instabilities relevant to AdS/CFT correspondence.

Fisher information metric characterizes the system's information geometry.

Abstract

We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of $N$ coupled Pais-Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.