Correlations between a Hawking particle and its partner in a 1+1D Bose-Einstein condensate analog black hole

TL;DR

This paper investigates the correlations between Hawking particles and their partners in a 1+1D Bose-Einstein condensate analog black hole by analyzing the density-density correlation function and its Fourier transform across different models.

Contribution

It introduces a detailed analysis of the density-density correlation function in BEC analog black holes, highlighting the impact of the effective potential on mode equations and particle production.

Findings

Effective potential significantly affects correlation functions.

Particle production inside the black hole is nonthermal.

Presence of a peak related to particle production in some models.

Abstract

The Fourier transform of the density-density correlation function in a Bose-Einstein condensate (BEC) analog black hole is a useful tool to investigate correlations between the Hawking particles and their partners. It can be expressed in terms of $\langle ^{\text{out}}\hat{a}_{\text{up}}^{\text{ext}}\ ^{\text{out}}\hat{a}_{\text{up}}^{\text{int}} \rangle$, where $^{\text{out}}\hat{a}_{\text{up}}^{\text{ext}}$ is the annihilation operator for the Hawking particle and $^{\text{out}}\hat{a}_{\text{up}}^{\text{int}} $ is the corresponding one for the partner. This basic quantity is calculated for three different models for the BEC flow. It is shown that in each model the inclusion of the effective potential in the mode equations makes a significant difference. Furthermore, particle production induced by this effective potential in the interior of the black hole is studied for each model and shown to be nonthermal. An interesting peak that is related to the particle production and is present in some models is discussed.