Sonic black holes with thick horizons in BECs

arXiv:2607.11396 · gr-qc, cond-mat.quant-gas, hep-th · Submitted 2026-07-13 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Sonic black holes with thick horizons in BECs".

Kai: We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous,

Mira: First, who's behind it and why it matters.

Title and authors: Kai: So, we're diving into the paper "Sonic black holes with thick horizons in BECs," which sounds really interesting because it connects condensed matter physics to concepts from general relativity. I'm wondering what exactly they built and measured to get these acoustic black hole analogies going.

Mira: From a theoretical standpoint, it’s fascinating how they take the idea of a horizon in gravity and try to map it onto fluid dynamics within Bose-Einstein condensates, which is a solid foundation for exploring analogue gravity effects three.

Lev: I'm curious if these BEC setups are even practical for any kind of measurement; what's the physical setup we're looking at here?

Kai: Well, the paper focuses on simple one-dimensional models where the flow is stepwise homogeneous, which means they are creating acoustic black holes by gluing different regions together, and I want to know what cooled systems they used to realize these regions.

Mira: The authors are Pe˜nalver, De Vito, Balbinot, and Fabbri, and their focus on BECs comes from the fact that experimental work has already shown Hawking-like radiation in these systems by measuring density correlations five.

Lev: If we were to take these models to real hardware for error correction purposes, I'd need to know how stable those specific flow profiles are under realistic noise conditions.

Kai: Exactly; they’re concentrating on the case where there’s an extended sonic region, which they call a thick horizon, rather than just an infinitely thin one we see in some other scenarios.

Mira: That extended region is key because it allows for a richer physics to explore, moving beyond the simplest horizon models

thirteen–sixteen: .

The paper's summary: Kai: So, what does the core of this study actually say about these acoustic black holes? I’m trying to get a grasp on the main findings regarding particle creation and those density correlations.

Mira: Essentially, they are looking at how these BEC models create particles and how those particle creation events show up in the density-density correlation functions, which is presented as the key experimental signature for Hawking-like radiation

seven–eleven: .

Lev: If the paper finds a mechanism for particle creation, what kind of number are they talking about, and how does that compare to what we expect from standard QFT?

Kai: They concentrate on the number of created particles and use these correlation functions as the tool to identify Hawking-like radiation in these acoustic black holes.

Mira: The models they employ involve a condensate made by joining homogeneous regions that can be subsonic, supersonic, and sonic, which is a central feature of this paper one.

Lev: That structure sounds complex for actual implementation; how does the math simplify when you have all three regimes interacting?

The paper's improvements: Kai: I noticed the paper discusses what they suggest as improvements or next steps for these models, and I want to understand what those suggestions are in terms of making the physics more realistic.

Mira: They present a specific set of toy models consisting of gluing two regions with different natures, and then they build up to a model that includes all three different regions existing simultaneously one.

Lev: From an error correction standpoint, if we have these complex glued systems, how does the complexity affect the feasibility of simulating quantum error correction protocols on them?

Kai: They emphasize that in all these cases, particular emphasis is placed on those density correlation functions because they are the most basic experimental tool to study Hawking-like radiation in these settings.

Mira: The authors are guiding us toward a model where all three different regions—subsonic, supersonic, and sonic—are present at once to see the full effect one.

Lev: I worry that increasing the complexity of the regions just increases the computational cost exponentially when trying to run those simulations on current hardware.

Conclusion: Kai: So, wrapping up this discussion on "Sonic black holes with thick horizons in BECs," what are the main implications we should be considering for this line of research?

Mira: The main implication is that these BEC models provide a concrete way to study the density correlation functions, which is currently the experimental tool used to look for Hawking-like radiation in acoustic black holes one.

Lev: For error correction, if these analogies hold up, it means we might have new theoretical pathways for understanding how quantum information might be affected by strong non-linear dynamics.

Kai: It seems like this work lays a very specific groundwork by defining the necessary mathematical structure to test these acoustic black hole concepts using measurable density correlations.

Mira: Ultimately, this paper pushes the research toward more complex configurations where all three flow regimes coexist, which is essential for seeing a complete picture of Hawking-like effects in these systems one.

Lev: I think if they can show how the physics scales across these different regimes, it gives us a better idea of how robust any quantum information might be under extreme conditions.

Daniel Pe˜nalver, *Marco De Vito*, ×Roberto Balbinot, ×Alessandro Fabbri

Departamento de FĿ sica TeĿrica and IFIC, Universidad de Valencia-CSIC · Dipartimento di Fisica e Astronomia dell’Universit’a di Bologna · INFN sezioni di Bologna

gr-qc, cond-mat.quant-gas, hep-th

Submitted: 2026-07-13

Updated: 2026-09-29

Comments: 36 pages, 22 figures. Final version

Journal ref: Phys. Rev. D114 (2026), 065030

DOI: 10.1103/8hsh-96jl

Code: https://github.com/dapema2/numerical-stepwise-bec-solutions

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 71/100

The gist: We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous, concentrating on cases where an extended sonic region is

Key concepts

Acoustic Black Holes
These are simple one-dimensional models of black holes created by Bose-Einstein condensates where the fluid flow is stepwise homogeneous. They are used to explore analogue gravity effects.
Thick Horizon
This refers to an extended region in the acoustic black hole model, as opposed to an infinitely thin one. This extended region allows researchers to explore richer physics beyond simpler horizon models.
Density Correlation Functions
These functions are presented as the key experimental signature used to identify Hawking-like radiation in these BEC models. They show how particle creation events manifest in the density correlations.
Bose-Einstein Condensates (BECs)
BECs are the physical systems used to realize these acoustic black hole models. Experimental work has already shown Hawking-like radiation in these systems by measuring density correlations.

Terminology

Summary

We consider simple one dimensional models of acoustic black holes formed by Bose-Einstein condensates where the flow is stepwise homogeneous, concentrating on cases where an extended sonic region is present, i.e., a region where the flow velocity equals exactly the speed of sound, which can be thought of as acoustic black holes with a thick horizon. Particular attention will be devoted to the number of created particles and to the density-density correlation functions, these latter being at present time the experimental tool to identify Hawking like radiation in acoustic black holes.

In General Relativity a black hole (BH) is a region of space-time which is causally disconnected from the rest of the Universe. A BH-like behaviour can be simulated by a fluid which undergoes a transition from a subsonic motion to a supersonic one [1, 2]. We have an acoustic BH. The transition region, where the speed of the flow equals the speed of sound, is called in analogy the sonic horizon. Unlike in gravity, one is not limited in this case to consider the transition from subsonic to supersonic regime to occur on an infinitely thin surface. By manipulating the external setup, one can envisage situations in which the speed of the flow equals the speed of sound over a layer of finite extension. We have a thick sonic horizon.

Among many condensed matter systems proposed as candidates to construct an acoustic BH, those formed by Bose-Einstein condensates (BECs) are the most promising, since for them one has experimentally shown the presence of Hawking-like radiation [5, 6] by measuring its associated density correlations functions [7–11].

In this paper we consider simple toy models of acoustic BHs where an extended sonic region is present (preliminary results were presented in [12]). The models we have in mind consist of a condensate formed by gluing homogeneous regions which can be subsonic, supersonic and also sonic. In section (II) we give a short introduction to the properties of homogeneous BECs in one spatial dimension, focusing on the difference in the dispersion relation corresponding to the three cases analysed (subsonic, supersonic, sonic). In section (III) models consisting in gluing two regions of different nature are examined and compared. Finally in section (IV) a model in which all three different regions are present is discussed. In all cases particular emphasis will be devoted to the density correlation functions, which are the basic experimental tool to study Hawking-like radiation in these settings.

Using standard BEC theory, one decomposes the basic boson field operator as:

Ψ(ˆ t, ⃗x) = Ψ0(⃗x) [1 + ϕˆ(t, ⃗x)], (2.1)

where the condensate is described by the macroscopic ground state wave function Ψ0 which satisfies the Gross-Pitaevskii (GP) equation:

iħ ∂Ψ0 / ∂t = −ħ2/2m ∇⃗ 2 + Vext + gΨ2 Ψ0. (2.2)

The fluctuation field ϕˆ describes small fluctuations above the condensate and represents the non condensed part of the system, satisfying the Bogoliubov-de Gennes (BdG) equation:

iħ ∂ϕˆ / ∂t = − ħ2/2∇⃗ 2 + ħ2/m∇⃗ Ψ0/Ψ0∇! ϕˆ + ng(ϕˆ + ϕˆ†. (2.3)

In a homogeneous 1D (quasi) condensate, the condensate wave function can be written as:

Ψ0 = √neik0x−ω0t, (2.4)

where v = ħk0/m is the flow velocity and ħω0 = ħ2/2k2/0/(2m) + gn + Vext. The fluctuation field ϕˆ can be expanded as:

ϕˆ(t, x) = Xj h aˆjϕj (t, x) + ˆa†jφ∗j (t, x), i, (2.5)"

where ˆa and ˆa† are annihilation and creation operators which satisfy the standard boson commutation rules [ˆai, a†j] = δij, and all the other commutators vanish. The modes ϕ, φ satisfy the equations:

i(∂t + v∂x) + ξc2/∂2x − c/ξϕj = c/ξφj (2.6)

−i(∂t + v∂x) + cξ2/ ∂2x − c/ξφj = c/ξϕj, (2.7)

where c = qgn/m is the speed of sound and ξ = ħmc is the healing length.

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed this paper, Sonic black holes with thick horizons in BECs, which explores Hawking-like radiation in one-dimensional Bose-Einstein Condensates (BECs) modeled as acoustic black holes with extended (thick) sonic horizons.

Here are the specific improvements for an AI system based on this research, categorized by capability:

The improved AI system, leveraging the mathematical framework and numerical results from this paper, can perform the following advanced tasks:

  1. Enhanced Simulation of Condensed Matter Analogies:

  2. Advanced Phenomenological Modeling & Parameter Estimation:

  3. Predictive Analysis of Correlation Functions (Experimental Signatures):

  4. Robust Model Comparison and Validation:

The specific capabilities for each area are as follows:

  1. Enhanced Simulation of Condensed Matter Analogies:

  2. Advanced Phenomenological Modeling & Parameter Estimation:

  3. Predictive Analysis of Correlation Functions (Experimental Signatures):

  4. Robust Model Comparison and Validation:

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