Scrambling time for analogue black holes embedded in AdS space

TL;DR

This paper proposes a thought experiment using analogue black holes in AdS space to measure the scrambling time, demonstrating how perturbations exponentially affect entanglement and relate to black hole entropy.

Contribution

It introduces a novel approach to test scrambling time using analogue black holes and clarifies the relationship between perturbations, entanglement destruction, and entropy.

Findings

Scrambling time scales logarithmically with black hole entropy.

Shock waves significantly alter the thermofield double state over time.

The approach provides a testable theoretical framework for scrambling in analogue systems.

Abstract

We propose a gedanken experiment on realizing thermofield double state (TFD) by using analog black holes and provide an approach to test the scrambling time. Through this approach, we demonstrate clearly how shock wave changes the TFD state as time evolves. As the whole system evolves forward in time, the perturbation of space-time geometry will increase exponentially. Finally, it will destroy the entanglement between the two states of the thermal field, and the mutual information between them is reduced to zero in the time scale of scrambling. The results show that for perturbations of analogue black holes embedded in AdS space, the scale of the scrambling time is closely related to the logarithm of entropy of the black hole. The results provide further theoretical argument for the scrambling time, which can be further falsified in experiments.