Slow scrambling in sonic black holes

TL;DR

This paper investigates quantum information scrambling in sonic black holes modeled by condensates, revealing they are slow scramblers with power-law OTOC growth, contrasting with astrophysical black holes.

Contribution

It provides an analytical framework for studying Hawking emission and OTOCs in sonic black holes, demonstrating their slow scrambling behavior.

Findings

OTOCs grow as t^2, indicating slow scrambling.

Sonic black holes differ from astrophysical ones in scrambling dynamics.

Analytical treatment based on Bogolyubov theory effectively describes quantum fluctuations.

Abstract

We study from the perspective of quantum information scrambling an acoustic black hole modelled by two semi-infinite, stationary, one dimensional condensates, connected by a spatial step-like discontinuity, and flowing respectively at subsonic and supersonic velocities. We develop a simple analytical treatment based on Bogolyubov theory of quantum fluctuations which is sufficient to derive analogue Hawking emission, and we compute out-of-time order correlations (OTOCs) of the Bose density field. We find that sonic black holes are slow scramblers contrary to their astrophysical counterparts: this manifests in a power law growth $\propto t^2$ of OTOCs in contrast to the exponential increase in time expected for fast scramblers.