Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that in a one-dimensional Bose-Einstein condensate analogue black hole, the Hawking-partner correlation spectrum departs significantly from a thermal Bose distribution at finite wavelengths, while the long-wavelength…

desk verdict A genuinely new completeness argument makes this a serious analogue-gravity paper, but the headline non-thermality claim currently rests on an unlabeled zero-temperature curve compared with a finite-temperature experiment. read the letter →

arxiv 1909.02509 v2 pith:ENFAJ2TU submitted 2019-09-05 cond-mat.quant-gas gr-qc

M. Isoard , N. Pavloff This is my paper · ORCID
classification cond-mat.quant-gasgr-qc
keywords analogueHawkingradiationBose-EinsteincondensatedensitycorrelationsthermalityzeromodesevanescentchannelsBogoliubovtheorytemperature
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the analogue Hawking radiation produced at a sonic horizon in a one-dimensional Bose-Einstein condensate is not thermal once all quantum fluctuation channels are treated on the same footing. Using a complete mode expansion that includes evanescent channels and the two zero modes tied to the broken U(1) symmetry, the authors reproduce the measured density correlation pattern around the horizon. They then show that the Hawking-partner correlation spectrum extracted with the correct frequency-dependent windowing departs significantly from a Bose thermal distribution at finite wavelengths, while its long-wavelength slope still fixes the Hawking temperature. If correct, this settles the apparent tension between theory and experiment and identifies the thermal-looking spectrum reported previously as an artifact of an approximate Fourier analysis.

What carries the argument

The load-bearing object is the complete expansion (3) of the fluctuation field, which adds the zero modes $\hat{P}$ and $\hat{Q}$ — the global phase degree of freedom and its conjugate, required for the canonical commutation relation — and the evanescent channel $u|_{\mathrm{eva}}$ to the standard Bogoliubov modes $U$, $D_1$, $D_2$. On top of this, the argument rests on the Fourier relation (5) between $G_2(x,x')$ and the Hawking-partner amplitude, combined with the frequency-dependent windowing condition (7), $L_u/|V_{g,H}(\omega)| = L_d/V_{g,P}(\omega)$, which fixes the integration rectangle by equal group-velocity traversal times. This windowing is what makes the extracted correlation agree with the exact scattering amplitude; the previously used $\omega$-independent windowing is what produces the spurious thermal spectrum.

What would settle it

Re-analyze the experimental data of Ref. [22] using the frequency-dependent windowing condition (7): if the extracted Hawking-partner correlation follows a thermal Bose distribution across the full measured frequency range, the claimed departure from thermality is refuted. A complementary check would compute $G_2$ from an incomplete basis that omits the zero modes and see whether it still matches the measured correlation map; matching would show the zero modes are not essential.

Watch

Extended reading notes

Core claim

The central claim is that the Hawking-partner correlation signal in the step-like BEC analogue black hole, computed from the density correlation function $G_2$ through the Fourier relation (5), deviates from the thermal Bose form $n_{\mathrm{TH}}(\omega)[1+n_{\mathrm{TH}}(\omega)]$ at finite frequencies. The deviation becomes visible only when $G_2$ is built from a complete basis for the quantum fluctuations, including the evanescent channel and the zero-mode operators $\hat{P}$ and $\hat{Q}$; omitting these pieces leaves the basis incomplete and produces a different, apparently thermal spectrum. The paper further shows that the experimental data of Ref. [22] are reproduced in real space by this complete calculation, and that the thermal conclusion of that experiment follows from replacing the frequency-dependent windowing condition (7) with a wavelength-independent one. Within the model, the Hawking temperature remains well defined from the low-frequency slope, but the radiation is not globally thermal.

Load-bearing premise

The load-bearing premise is that the quantum field can be split into a classical condensate plus small linearized Bogoliubov fluctuations, an approximation the paper acknowledges is not strictly valid in one dimension and whose justification is borrowed from an earlier analysis rather than established here.

Editorial extensions

If this is right

  • The measured density correlations around the horizon can be reproduced at zero temperature, provided evanescent channels and zero modes are included; an incomplete basis misses the correct correlation pattern.
  • The Hawking temperature remains a well-defined observable: it is fixed by the long-wavelength limit of the correlation signal even though the full spectrum is non-thermal.
  • The thermal spectrum reported in Ref. [22] is reinterpreted as an artifact of an unfounded, $\omega$-independent integration window; using the group-velocity windowing (7) predicts a measurable departure from thermality.
  • Re-analyzing the published experimental data with the proposed windowing should reveal the non-thermal behaviour predicted here.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the departure is confirmed, thermality in analogue systems should be treated as a long-wavelength property, not a global one; other analogue platforms may show similar finite-wavelength deviations even where the low-frequency Hawking temperature is clean.
  • The same complete-basis corrections could affect other observables built from the quantum fluctuations, such as entanglement or non-separability measures, not just the density correlation function.
  • The windowing prescription provides a concrete, testable data-analysis protocol: apply the group-velocity condition (7) to existing experimental correlation maps and compare the extracted spectrum with the exact scattering calculation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies quantum fluctuations in a one-dimensional Bose-Einstein condensate realizing an analogue acoustic black hole with a step potential. The authors develop a linearized Bogoliubov description of the fluctuations using a complete basis that includes evanescent channels and zero modes, compute the density correlation function G2, and show that it reproduces the measured correlations of Ref. [22] once finite-temperature effects at kBT = 0.2gnu are included. They then use a Fourier relation, Eq. (5), to extract the Hawking-partner correlation signal from G2, compare it with the experimental data, and argue that the exact theoretical signal deviates from a thermal Bose distribution at finite wavelengths. The main claim is that the apparent thermality in previous analyses is an artifact of an unfounded long-wavelength windowing, while the long-wavelength slope still determines the Hawking temperature.

Significance. If correct, the paper provides a concrete mechanism for departures from thermality in analogue Hawking radiation, settles the role of zero modes and evanescent channels in the density-correlation analysis, and offers a falsifiable prescription for re-analyzing existing experimental data. The calculation is well posed: the red curve in Fig. 4 follows from the model with no free fitting, and the real-space agreement in Fig. 3 is a genuine nontrivial success. The paper also honestly acknowledges its main approximations, namely the 1D Bogoliubov separation and the borrowing of its justification from the authors' own earlier work. The central claim is timely and relevant to the active debate on analogue Hawking radiation in Bose-Einstein condensates.

major comments (4)
  1. [Fig. 4 and Eq. (5)] The caption of Fig. 4 does not state the temperature at which the red theoretical curve is computed. Figure 3 shows that the zero-temperature G2 differs visibly from the finite-temperature G2 at kBT = 0.2gnu (T ≃ 1.9TH), and Eq. (5) Fourier-transforms G2, so the extracted |S0⟨ĉU ĉD2⟩|² is temperature dependent. Since the experiment of Ref. [22] is performed at T ≈ 1.9TH and fig. 3 shows that the finite-temperature curve is the one matching the experimental data, a zero-temperature red curve cannot be the proper model for the experimental comparison. The claimed departure from thermality therefore requires, but does not provide, the finite-temperature version of the red curve.
  2. [‘Departing from thermality’ and Eq. (8)] The blue thermal curve is constructed using exactly the type of approximation the paper criticizes: an ω-independent ratio kH/kP and neglect of the d1|out channel. This is acknowledged to be self-consistent within the long-wavelength approach, but the central assertion that this procedure is ‘unfounded’ is not supported by a quantitative demonstration that the proposed windowing (7) changes the experimental dots in Fig. 4. The authors appropriately propose a re-analysis of the data of Ref. [22] as future work, but that means the paper's headline claim is a prediction rather than a completed verification; the manuscript should state this distinction explicitly and, ideally, provide the finite-temperature processing of the experimental data.
  3. [Fig. 3 and Eq. (4)] The finite-temperature calculation underlying the orange curve in Fig. 3 is not derived. The text states that kBT = 0.2gnu gives T ≃ 1.9TH, but does not explain how thermal occupations are introduced into the correlation functions in the presence of the zero-mode state |BH⟩, nor how this value of kBT was chosen. Since the temperature dependence of G2 propagates through Eq. (5) into the Hawking-partner signal, this missing specification is load-bearing for the central claim and must be supplied.
  4. [Eqs. (2)–(3)] The validity of splitting the 1D field into a classical condensate plus linearized Bogoliubov fluctuations is delegated to Ref. [31]. Because every correlation function in the paper, including the departure-from-thermality prediction, relies on this linearization, the manuscript should include at least a concise statement of the density regime where the approximation is controlled, or a benchmark against an independent 1D method. As written, the supporting argument is borrowed from the authors' own earlier work rather than established here.
minor comments (5)
  1. [Fig. 3 caption] The caption should define TH explicitly and state the upstream density nu used to set kBT = 0.2gnu, so that the value T ≃ 1.9TH is reproducible without referring to the experimental paper.
  2. [Fig. 4 caption and text] The text refers to a ‘bluish region’ and a ‘blue region’ interchangeably; please use a single term consistently, and clarify whether the blue region corresponds to the 10% accuracy domain or to the approximation used for the blue curve.
  3. [Eq. (8)] The notation nTH(ω) is introduced without an equation number or an explicit definition; please state that it denotes the Bose factor [exp(ℏω/kBTH) − 1]⁻¹.
  4. [General] There are minor language issues, including ‘one is lead to introduce’ (should be ‘led’) and ‘degree of liberty’ (should be ‘degree of freedom’).
  5. [Conclusion] The word ‘unfounded’ for the previous windowing procedure is strong; given that the authors show the procedure is internally self-consistent but inaccurate at finite dispersion, a phrase such as ‘not justified by the exact dispersion’ would be more precise and less contentious.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the non-thermal prediction is a computed consequence of the model, not an input or a renamed fit.

full rationale

The central derivation is self-contained. The paper constructs the Bogoliubov mode expansion (Eq. 3), including zero modes needed for the canonical commutation relation, and computes G2 directly from the chosen quantum state. The extraction of the Hawking-partner correlation via Eq. (5) is an identity relating a Fourier window of G2 to an S-matrix element; it is not fitted to the claim of non-thermality. The blue thermal curve is explicitly obtained by making two long-wavelength approximations (omega-independent wavevector ratio and neglect of the d1|out channel), while the red curve uses the full expression without those approximations. The departure from thermality is therefore a consequence of the dispersion relation and the scattering calculation, not an assumption. The comparison with the experiment of Ref. [22] is an external benchmark, and the parameters such as Vd/cd = 2.90 are chosen to match the experimental configuration, which is standard benchmarking rather than circular fitting. The self-citations (Refs. [31], [42], [44]) support technical ingredients such as the zero-mode structure and dispersion relations; none of them is invoked as a uniqueness theorem forbidding alternatives, and none is used to define the non-thermal result. The temperature ambiguity of the red curve in Fig. 4 is a legitimate missing-support or correctness concern, but it is not a circularity: the model's red curve is not defined in terms of the experimental data points it is compared with. No derived quantity reduces by construction to an input parameter, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The model introduces no new physical entities; the zero modes are standard Goldstone modes of the broken U(1) symmetry, not new particles or forces. The main input knobs are the flow ratio (set by the experimental configuration) and the finite-temperature parameter used in the comparison. Several domain assumptions about mode completeness and 1D validity carry the calculation.

free parameters (2)
  • Upstream flow ratio Vu/cu (or downstream Vd/cd = 2.90) = Vd/cd = 2.90; Vu/cu = 0.59
    Chosen to reproduce the experimental configuration of Ref. [22]; it sets the horizon strength and affects all computed correlations and the Hawking temperature.
  • Finite temperature kBT (Fig. 3) = 0.2 g n_u (T ~ 1.9 T_H)
    The finite-temperature curve used for comparison with the experimental data is presented as a fixed value with no derivation; it is effectively chosen to match the measured G2.
assumptions (7)
  • domain assumption The classical field plus linearized quantum fluctuations (Bogoliubov) splitting is a valid approximation in one dimension over the relevant density range.
    Invoked after Eq. (2); the paper states the splitting is not strictly valid in 1D and cites its own Ref. [31] for validity. All G2 and spectrum results depend on this.
  • domain assumption The asymptotic mode decomposition U, D1, D2 plus zero modes P and Q forms a complete basis for the quantum fluctuations.
    Stated around Eq. (3); completeness is needed to satisfy [psi, psi-dagger] = delta(x-y) and to get the correct G2. The paper argues omitting zero modes would be incomplete.
  • domain assumption The quantum state of the analogue horizon is the zero-excitation state |BH> with P|BH>=0 and b_L|BH>=0.
    Introduced after Eq. (3); this defines the vacuum around which correlations are computed. Finite-temperature effects are patched in afterwards using earlier references.
  • domain assumption Steinhauer's Fourier relation (Eq. 5) with the frequency-dependent windowing (Eq. 7) correctly extracts the Hawking-partner scattering amplitude from G2.
    The paper states it has checked that once prescription (7) is fulfilled, formula (5) is very well verified, with the check deferred to Supplemental Material [46]. If wrong, the red curve in Fig. 4 would not represent the true correlation spectrum.
  • domain assumption The background step potential and densities are described by a half dark soliton plus plane wave with matching obtained from the Gross-Pitaevskii equation.
    Used to construct the scattering modes; the shape determines the S-matrix and the zero-mode function q(x).
  • domain assumption The experimental data of Ref. [22] and its quoted flow velocities and sound speeds are accurate.
    The comparison and the input Hawking temperature in Eq. (8) rely on those measurements.
  • standard math Bogoliubov dispersion and S-matrix unitarity (|Sd2,d2|^2 = 1 + |Su,d2|^2 + |Sd1,d2|^2).
    Used to derive Eq. (8) and to interpret the scattering coefficients.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate." pith.science (2026). https://pith.science/paper/ENFAJ2TU

@misc{pith2026190902509,
  author       = {Pith},
  title        = {Pith review of: Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ENFAJ2TU}},
  note         = {Machine review of arXiv:1909.02509}
}
read the original abstract

We study the quantum fluctuations in a one dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.

Figures

Figures reproduced from arXiv: 1909.02509 by the authors.

Figure 1
Figure 1. FIG. 1: Sketch of the different channels contributing to the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Red solid line: zero temperature density correlation [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4: Hawking-partner correlation signal represented as a [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Doppler shifted Hawking radiation from acoustic black holes in ultra-relativistic heavy-ion collisions

    hep-ph 2025-09 conditional novelty 6.0 of 10

    Even when the central flow is boost invariant, large-rapidity deviations can slow the acoustic horizon's recession, giving finite redshift Hawking radiation that may affect momentum distributions.

Reference graph

Works this paper leans on

59 extracted references · 33 canonical work pages · cited by 1 Pith paper

  1. [22]

    J. R. M. de Nova, K. Golubkov, V. I. Kolobov, and J. Steinhauer, Nature (London) 569, 688 (2019) doi:10.1038/s41586-019-1241-0

    work page doi:10.1038/s41586-019-1241-0 2019

  2. [31]

    Fabbri and N

    A. Fabbri and N. Pavloff SciPost Phys. 4, 019 (2018) doi:10.21468/SciPostPhys.4.4.019

    work page doi:10.21468/scipostphys.4.4.019 2018

  3. [1]

    S. W. Hawking, Nature (London) 248, 30 (1974) doi:10.1038/248030a0; Commun. Math. Phys. 43, 199 (1975) doi:10.1007/BF02345020

    doi:10.1038/248030a0 1974

  4. [2]

    Visser, Phys

    M. Visser, Phys. Rev. Lett. 80, 3436 (1998) doi:10.1103/PhysRevLett.80.3436

    work page doi:10.1103/physrevlett.80.3436 1998

  5. [3]

    W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981) doi:10.1103/PhysRevLett.46.1351

    doi:10.1103/physrevlett.46.1351 1981

  6. [4]

    Rousseaux, C

    G. Rousseaux, C. Mathis, P. Ma¨ ıssa, T. G. Philbin, and U. Leonhardt, New J. Phys. 10, 053015 (2008) doi:10.1088/1367-2630/10/5/053015

    doi:10.1088/1367-2630/10/5/053015 2008

  7. [5]

    Weinfurtner, E

    S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, and G. A. Lawrence, Phys. Rev. Lett106, 021302 (2011) doi:10.1103/PhysRevLett.106.021302

    doi:10.1103/physrevlett.106.021302 2011

  8. [6]

    Euv´ e, F

    L.-P. Euv´ e, F. Michel, R. Parentani, T. G. Philbin, and G. Rousseaux, Phys. Rev. Lett. 117, 121301 (2016) doi:10.1103/PhysRevLett.117.121301

    work page doi:10.1103/physrevlett.117.121301 2016

Show all 59 references
  1. [7]

    Cardoso, A

    V. Cardoso, A. Coutant, M. Richartz, and S. Weinfurtner, Phys. Rev. Lett. 117, 271101 (2016) doi:10.1103/PhysRevLett.117.271101

    2016 doi

  2. [8]

    Torres, S

    T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, Nat. Phys. 13, 833 (2017) doi:10.1038/nphys4151

    2017 doi

  3. [9]

    Euv´ e, S

    L.-P. Euv´ e, S. Robertson, N. James, A. Fabbri, and G. Rousseaux, arXiv:1806.05539

    arXiv

  4. [10]

    Goodhew, S

    H. Goodhew, S. Patrick, C. Gooding, and S. Weinfurtner, arXiv:1905.03045

    1905 arXiv

  5. [11]

    Philbin, C

    T.G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. K¨ onig, and U. Leonhardt, Science 319, 1367 (2008) doi:10.1126/science.1153625

    2008 doi

  6. [12]

    Belgiorno, S

    F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio Phys. Rev. Lett. 105, 203901 (2010) doi:10.1103/PhysRevLett.105.203901

    2010 doi

  7. [13]

    Rubino, F

    E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kole- sik and D. Faccio, New J. Phys. 13, 085005 (2011) doi:10.1088/1367-2630/13/8/085005

    2011 doi

  8. [14]

    Elazar, V

    M. Elazar, V. Fleurov, and S. Bar-Ad Phys. Rev. A 86, 063821 (2012) doi:10.1103/PhysRevA.86.063821

    2012 doi

  9. [15]

    K. E. Webb, M. Erkintalo, Y. Xu, N. G. R. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, Nat. Commun. 5, 4969 (2014) doi:10.1038/ncomms5969

    2014 doi

  10. [16]

    Vocke, C

    D. Vocke, C. Maitland, A. Prain, K. E. Wilson, F. Bian- calana, E. M. Wright, F. Marino, and D. Faccio, Optica 5, 1099 (2018) doi:10.1364/OPTICA.5.001099

    2018 doi

  11. [17]

    Drori, Y

    J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, and U. Leonhardt, Phys. Rev. Lett. 122, 010404 (2019) doi:10.1103/PhysRevLett.122.010404

    2019 doi

  12. [18]

    Nguyen, D

    H.S. Nguyen, D. Gerace, I. Carusotto, D. San- vitto, E. Galopin, A. Lemaˆ ıtre, I. Sagnes, J. Bloch, and A. Amo, Phys. Rev. Lett. 114, 036402 (2015) doi:10.1103/PhysRevLett.114.036402

    2015 doi

  13. [19]

    Lahav, A

    O. Lahav, A. Itah, A. Blumkin, C. Gordon, S. Rinott, A. Zayats, and J. Steinhauer, Phys. Rev. Lett. 105, 240401 (2010) doi:10.1103/PhysRevLett.105.240401

    2010 doi

  14. [20]

    Steinhauer, Nat

    J. Steinhauer, Nat. Phys. 10, 864 (2014) doi:10.1038/nphys3104

    2014 doi

  15. [21]

    Steinhauer, Nat

    J. Steinhauer, Nat. Phys. 12, 959 (2016) doi:10.1038/nphys3863

    2016 doi

  16. [23]

    Michel and R

    F. Michel and R. Parentani, Phys. Rev. A 91, 053603 (2015) doi:10.1103/PhysRevA.91.053603

    2015 doi

  17. [24]

    Michel, J.-F

    F. Michel, J.-F. Coupechoux, and R. Parentani Phys. Rev. D 94, 084027 (2016) doi:10.1103/PhysRevD.94.084027

    2016 doi

  18. [25]

    Tettamanti, S

    M. Tettamanti, S. L. Cacciatori, A. Parola and I. Carusotto, EPL 114, 60011 (2016) doi:10.1209/0295- 5075/114/60011

    2016 doi

  19. [26]

    J. R. M. de Nova, S. Finazzi, and I. Carusotto, Phys. Rev. A 94, 043616 (2016) doi:10.1103/PhysRevA.94.043616

    2016 doi

  20. [27]

    Finke, P

    A. Finke, P. Jain, and S. Weinfurtner, New J. Phys. 18, 113017 (2016) doi:10.1088/1367-2630/18/11/113017

    2016 doi

  21. [28]

    Y.-H. Wang, T. Jacobson, M. Edwards, and C. W. Clark, SciPost Phys. 3, 022 (2017) doi:10.21468/SciPostPhys.3.3.022

    2017 doi

  22. [29]

    Parola, M

    A. Parola, M. Tettamanti, and S. L. Cacciator, EPL 119, 50002 (2017) doi:10.1209/0295-5075/119/50002

    2017 doi

  23. [30]

    Robertson, F

    S. Robertson, F. Michel, and R. Parentani, Phys. Rev. D 96, 045012 (2017) doi:10.1103/PhysRevD.96.045012

    2017 doi

  24. [32]

    Coutant and S

    A. Coutant and S. Weinfurtner, Phys. Rev. D 97, 025006 (2018) doi:10.1103/PhysRevD.97.025006

    2018 doi

  25. [33]

    J. M. Gomez Llorente and J. Plata, J. Phys. B: At. Mol. Opt. Phys. 52 075004 (2019) doi:10.1088/1361- 6455/ab0bcb

    2019 doi

  26. [34]

    Leonhardt, Ann

    U. Leonhardt, Ann. Phys. (Berlin) 530, 1700114 (2018) doi:10.1002/andp.201700114

    2018 doi

  27. [35]

    Steinhauer, Ann

    J. Steinhauer, Ann. Phys. (Berlin) 530, 1700459 (2018) doi:10.1002/andp.201700459

    2018 doi

  28. [36]

    W. G. Unruh, Phys. Rev. D 51, 2827 (1995) doi:10.1103/PhysRevD.51.2827

    1995 doi

  29. [37]

    Corley and T

    S. Corley and T. Jacobson, Phys. Rev. D 54, 1568 (1996) doi:10.1103/PhysRevD.54.1568

    1996 doi

  30. [38]

    Corley, Phys

    S. Corley, Phys. Rev. D 55, 6155 (1997) doi:10.1103/PhysRevD.55.6155

    1997 doi

  31. [39]

    Jacobson, Phys

    T. Jacobson, Phys. Rev. D 44, 1731 (1991) doi:10.1103/PhysRevD.44.1731

    1991 doi

  32. [40]

    Leboeuf, N

    P. Leboeuf, N. Pavloff and S. Sinha, Phys. Rev. A 68, 063608 (2003) doi:10.1103/PhysRevA.68.063608

    2003 doi

  33. [41]

    Macher and R

    J. Macher and R. Parentani, Phys. Rev. A 80, 043601 (2009) doi:10.1103/PhysRevA.80.043601

    2009 doi

  34. [42]

    Recati, N

    A. Recati, N. Pavloff and I. Carusotto, Phys. Rev. A 80, 043603 (2009) doi:10.1103/PhysRevA.80.043603

    2009 doi

  35. [43]

    Coutant, R

    A. Coutant, R. Parentani, and S. Finazzi, Phys. Rev. D 85, 024021 (2012) doi:10.1103/PhysRevD.85.024021

    2012 doi

  36. [44]

    Larr´ e, A

    P.- ´E. Larr´ e, A. Recati, I. Carusotto, and N. Pavloff, Phys. Rev. A 85, 013621 (2012) doi:10.1103/PhysRevA.85.013621

    2012 doi

  37. [45]

    Boiron, A

    D. Boiron, A. Fabbri, P.- ´E. Larr´ e, N. Pavloff, C. I. West- brook, and P. Zi´ n, Phys. Rev. Lett.115, 025301 (2015) 6 doi:10.1103/PhysRevLett.115.025301

    2015 doi

  38. [46]

    See Supplemental Material [url] which recalls previous results, details some characteristics of the zero modes and of the analysis of the Hawking spectrum and includes Refs. [47–49]

  39. [47]

    Villain, M

    P. Villain, M. Lewenstein, R. Dum, Y. Castin, L. You, A. Imamo˘ glu, and T. A. B. Kennedy, J. Mod. Optics44, 1775 (1997), doi:10.1080/09500349708231846

    1997 doi

  40. [48]

    Bilas and N

    N. Bilas and N. Pavloff Phys. Rev. A 72, 033618 (2005), doi:10.1103/PhysRevA.72.033618

    2005 doi

  41. [49]

    Deuar, A

    P. Deuar, A. G. Sykes, D. M. Gangardt, M. J. Davis, P. D. Drummond and K. V. Kheruntsyan, Phys. Rev. A 79, 043619 (2009), doi:10.1103/PhysRevA.79.043619

    2009 doi

  42. [50]

    Lewenstein and L

    M. Lewenstein and L. You, Phys. Rev. Lett. 77, 3489 (1996) doi:10.1103/PhysRevLett.77.3489

    1996 doi

  43. [51]

    Leonhardt, T

    U. Leonhardt, T. Kiss, and P. ¨Ohberg, J. Opt. B: Quan- tum Semiclassical. Opt. 5, S42 (2003) doi:10.1088/1464- 4266/5/2/357

    2003 doi

  44. [52]

    Ring and P

    P. Ring and P. Shuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, 1980)

    1980

  45. [53]

    J. P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986)

    1986

  46. [54]

    Balbinot, A

    R. Balbinot, A. Fabbri, S. Fagnocchi, A. Recati and I. Carusotto, Phys. Rev. A 78, 021603(R) (2008) doi:10.1103/PhysRevA.78.021603

    2008 doi

  47. [55]

    Carusotto, S

    I. Carusotto, S. Fagnocchi, A. Recati, R. Balbinot and A. Fabbri, New J. Phys. 10, 103001 (2008) doi:10.1088/1367-2630/10/10/103001

    2008 doi

  48. [56]

    Steinhauer, Phys

    J. Steinhauer, Phys. Rev. D 92, 024043 (2015) doi:10.1103/PhysRevD.92.024043

    2015 doi

  49. [57]

    C. J. Pethick and H. Smith, Bose-Einstein Condensa- tion in Dilute Gases, (Cambridge University Press, Cam- bridge, England, 2002)

    2002

  50. [58]

    L. P. Pitaevskii and S. Stringari, Bose-Einstein Conden- sation, International Series of Monographs on Physics, (Oxford University Press, Oxford, United Kingdom, 2016)

    2016

  51. [59]

    J. R. M. de Nova, F. Sols and I. Zapata, New. J. Phys. 17, 105003 (2015) doi:10.1088/1367-2630/17/10/105003

    2015 doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.