Evanescent Modes and Step-like Acoustic Black Holes

TL;DR

This paper investigates evanescent modes and Hawking radiation in a Bose-Einstein condensate model of an acoustic black hole with a step-like horizon, revealing how evanescent solutions influence observable phenomena and potential information leakage.

Contribution

It introduces the analysis of evanescent solutions in acoustic black holes with step-like horizons and explores their impact on Hawking radiation and information transfer.

Findings

Evanescent modes decay outside the horizon and modulate observables.

Superpositions of ingoing modes can cancel Hawking flux externally.

Evanescent modes may enable information leakage when quasiparticle interactions are considered.

Abstract

We consider a model of an acoustic black hole formed by a quasi-one dimensional Bose-Einstein condensate with a step-like horizon. This system is analyzed by solving the corresponding Bogoliubov-de Gennes equation with an appropriate matching condition at the jump. When the step is between a subsonic and supersonic flow, a sonic horizon develops and in addition to the scattering coefficients we compute the distribution of the accompanying analogue Hawking radiation. Additionally, in response to the abrupt variation in flow and non-linear Bogoliubov dispersion relation, evanescent solutions of the Bogoliubov-de Gennes equation also appear and decay out from the horizon. We bound this decay length and show that these modes produce a modulation of observables outside the event horizon by their interference with outgoing Hawking flux. We go further and find specific superpositions of ingoing eigenmodes which exhibit coherent cancellation of the Hawking flux outside the horizon but nevertheless have evanescent support outside the black hole. We conclude by speculating that when quasiparticle interactions are included, evanescent modes may yield a leakage of information across the event horizon via interactions between the real outgoing Hawking flux and the virtual evanescent modes, and that we may expect this as a generic feature of models which break Lorentz invariance at the UV (Planck) scale.