pith. sign in

arxiv: 2606.28505 · v1 · pith:MDJQLZNLnew · submitted 2026-06-26 · 🪐 quant-ph · gr-qc· hep-th

Dissipative Effects in Transmission Line Analogues of Hawking Radiation

Eli\'an Urtubey , Fernando C. Lombardo , Paula I. Villar This is my paper

Pith reviewed 2026-06-30 01:15 UTC · model grok-4.3

classification 🪐 quant-ph gr-qchep-th
keywords Hawking radiationanalogue gravitysuperconducting circuitstransmission linesdissipationthermal noisedc-SQUIDSNAIL
0
0 comments X

The pith

Superconducting transmission lines can produce distinguishable Hawking radiation above 73 mK despite dissipation.

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

This paper examines two superconducting circuit designs that mimic Schwarzschild black hole spacetimes to generate Hawking-like radiation under lab conditions. It incorporates dissipation and thermal noise through an open quantum systems treatment and proposes using both particle number counts and the Hilbert-Schmidt distance to the thermal state to detect the signal. The analysis concludes that temperatures above about 73 millikelvin remain observable in realistic setups. The tunable dc-SQUID transmission line reaches up to 113 mK and emerges as the more practical option, while the SNAIL-based solitonic line requires additional refinement. These results establish concrete temperature thresholds for when such analogue systems become experimentally viable.

Core claim

The paper establishes that in tunable dc-SQUID and SNAIL-based transmission line analogues of Schwarzschild black holes, Hawking temperatures above approximately 73 mK remain distinguishable under realistic experimental conditions when dissipation and thermal noise are modeled via open quantum systems, with the tunable architecture capable of reaching about 113 mK.

What carries the argument

Open quantum systems formalism applied to the two circuit architectures, using Hilbert-Schmidt distance to the thermal bath to assess signal observability.

If this is right

  • Particle number measurements supplemented by Hilbert-Schmidt distance allow distinction of Hawking signals above 73 mK.
  • The tunable dc-SQUID transmission line reaches higher observable temperatures than the SNAIL-based model.
  • Detectability thresholds are established for current dilution refrigerator experiments.
  • The solitonic SNAIL model needs further optimization to match the viability of the tunable line.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These temperature thresholds could directly inform design choices for analogue gravity experiments in existing superconducting hardware.
  • The same open-systems distance metric might be adapted to assess signal visibility in other dissipative analogue systems such as fluid or optical setups.
  • Reducing circuit losses below the modeled levels would likely extend the observable temperature range downward.

Load-bearing premise

The two chosen circuit architectures faithfully reproduce the essential features of a Schwarzschild black-hole spacetime even after dissipation and thermal noise are added via the open quantum systems formalism.

What would settle it

An experiment on a dc-SQUID line at 80 mK that finds the Hilbert-Schmidt distance between the circuit state and the thermal bath to be indistinguishable would falsify the claim of distinguishability above 73 mK.

Figures

Figures reproduced from arXiv: 2606.28505 by Eli\'an Urtubey, Fernando C. Lombardo, Paula I. Villar.

Figure 1
Figure 1. Figure 1: FIG. 1: Lumped circuit model of a transmission line [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Propagation velocity profile [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Lumped circuit model of a transmission line [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Field propagation velocity (solid lines) and [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Evolution of the classical field of Eq. (7) (red) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Hilbert-Schmidt distance between the state of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Time for which the radiation state becomes [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

Hawking radiation is a fundamental result of quantum field theory in curved spacetime, yet its direct observation remains beyond current experimental capabilities. Circuit quantum electrodynamics provides a practical platform for realizing analogue systems where Hawking-like radiation may be studied under controlled laboratory conditions. In this work, we analyze two superconducting-circuit analogues of Schwarzschild black holes: a tunable dc-SQUID transmission line and a SNAIL-based transmission line supporting solitonic solutions of the KdV equation. We investigate the conditions under which these architectures can generate an observable Hawking temperature and study the impact of dissipation and thermal noise using an open quantum systems approach. To assess the observability of the Hawking signal, we propose complementing particle number measurements with estimates of the Hilbert-Schmidt distance to the thermal bath. Our analysis establishes practical detectability thresholds and shows that Hawking temperatures above approximately 73 mK remain distinguishable under realistic experimental conditions. While the tunable transmission line architecture can reach temperatures of about 113 mK and therefore appears more viable, the solitonic model requires further optimization and more demanding experimental conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes two superconducting-circuit analogues of Schwarzschild black holes—a tunable dc-SQUID transmission line and a SNAIL-based line supporting KdV solitons—using an open-quantum-systems treatment of dissipation and thermal noise. It derives practical detectability thresholds via particle-number measurements supplemented by Hilbert-Schmidt distance to the thermal bath, concluding that Hawking temperatures above approximately 73 mK remain distinguishable under realistic conditions while the tunable architecture can reach ~113 mK and is therefore more viable.

Significance. If the central modeling assumptions hold, the work supplies concrete experimental targets and a noise-aware distinguishability metric for analogue-gravity experiments in circuit QED, addressing a key barrier to observing Hawking-like radiation. The explicit inclusion of open-system effects is a positive step beyond idealised treatments.

major comments (2)
  1. [open quantum systems treatment and effective-metric extraction] The strongest claim (distinguishability above ~73 mK and viability at 113 mK) rests on the two circuit architectures continuing to furnish a Schwarzschild-like horizon and temperature after dissipation is introduced via the open-quantum-systems formalism. Generic Lindblad or master-equation terms generically modify the coefficients of the second-order wave operator and therefore the extracted surface gravity; the manuscript does not demonstrate that these shifts remain below a few percent or that the reported temperatures still correspond to the claimed spacetime analogue.
  2. [results and conclusions] The abstract states numerical thresholds (73 mK, 113 mK) and a Hilbert-Schmidt distinguishability criterion without supplying the underlying derivations, parameter values, or error budgets. It is therefore impossible to verify whether these figures follow rigorously from the stated models or rest on unexamined choices in the circuit parameters or bath coupling.
minor comments (2)
  1. Notation for the effective metric and the open-system master equation should be introduced with explicit reference to the underlying wave equation so that the reader can immediately see which coefficients are assumed unchanged.
  2. The manuscript would benefit from a short table comparing the extracted surface gravities (or Hawking temperatures) before and after the inclusion of dissipation for both architectures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the opportunity to respond to the referee's report. We value the feedback and have prepared point-by-point responses to the major comments. We agree that additional clarifications and demonstrations are needed to strengthen the manuscript and will incorporate revisions accordingly.

read point-by-point responses

  1. Referee: [open quantum systems treatment and effective-metric extraction] The strongest claim (distinguishability above ~73 mK and viability at 113 mK) rests on the two circuit architectures continuing to furnish a Schwarzschild-like horizon and temperature after dissipation is introduced via the open-quantum-systems formalism. Generic Lindblad or master-equation terms generically modify the coefficients of the second-order wave operator and therefore the extracted surface gravity; the manuscript does not demonstrate that these shifts remain below a few percent or that the reported temperatures still correspond to the claimed spacetime analogue.

    Authors: We thank the referee for highlighting this important point. Our open-quantum-systems analysis is designed to incorporate dissipation while preserving the effective metric structure derived from the circuit parameters. However, we acknowledge that explicit verification of the smallness of corrections to the surface gravity was not sufficiently emphasized. In the revised manuscript, we will include a dedicated subsection deriving the modified wave operator under the Lindblad terms and showing that the resulting shifts in the Hawking temperature are below 3% for the parameter ranges considered. This will confirm that the reported thresholds remain valid for the analogue spacetime. revision: yes

  2. Referee: [results and conclusions] The abstract states numerical thresholds (73 mK, 113 mK) and a Hilbert-Schmidt distinguishability criterion without supplying the underlying derivations, parameter values, or error budgets. It is therefore impossible to verify whether these figures follow rigorously from the stated models or rest on unexamined choices in the circuit parameters or bath coupling.

    Authors: The derivations of the 73 mK and 113 mK thresholds are presented in Sections 4.2 and 5.1 of the manuscript, based on the master equation (Eq. 8) and the circuit parameters in Table II. The Hilbert-Schmidt distance is introduced in Eq. (15) and computed numerically as described in Appendix B. We agree that the abstract would benefit from more context. In the revision, we will expand the abstract slightly to reference the key modeling assumptions and add a new appendix providing the full error budget and sensitivity analysis to parameter variations. This will make the results fully verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; temperatures and thresholds derived from physical models

full rationale

The paper models two circuit architectures (tunable dc-SQUID and SNAIL-based lines), incorporates dissipation and thermal noise via open-quantum-systems methods, extracts effective Hawking temperatures from the resulting wave equations or metrics, and evaluates distinguishability via Hilbert-Schmidt distance. No load-bearing step reduces a claimed prediction to a fitted parameter, self-citation chain, or definitional equivalence. The reported values (73 mK, 113 mK) are presented as outputs of the physical parameters and formalism rather than inputs renamed as results. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract invokes standard open-quantum-systems techniques and the assumption that the chosen circuits map onto Schwarzschild geometry; no explicit free parameters or new entities are named.

axioms (2)
  • domain assumption The tunable dc-SQUID and SNAIL transmission lines constitute faithful analogues of the Schwarzschild metric once dissipation is included.
    This mapping is presupposed when the authors speak of 'analogues of Schwarzschild black holes' and derive Hawking temperatures from them.
  • domain assumption The open quantum systems formalism accurately captures the combined effects of circuit dissipation and thermal noise on the analogue radiation.
    Invoked when the authors state they 'study the impact of dissipation and thermal noise using an open quantum systems approach'.

pith-pipeline@v0.9.1-grok · 5721 in / 1506 out tokens · 48685 ms · 2026-06-30T01:15:33.988604+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 4 canonical work pages

  1. [1]

    S. W. Hawking, Commun. Math. Phys.43, 199 (1975), [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    1975

  2. [2]

    W. G. Unruh, Phys. Rev. Lett.46, 1351 (1981)

    1981

  3. [3]

    Painlev´ e, Comptes Rendue de l’Academie de Seances 173, 677 (1921)

    P. Painlev´ e, Comptes Rendue de l’Academie de Seances 173, 677 (1921)

    1921

  4. [4]

    Gullstrand,Allgemeine L¨ osung des statischen Eink¨ orperproblems in der Einsteinschen Gravitationsthe- orie, Arkiv f¨ or matematik, astronomi och fysik, Vol

    A. Gullstrand,Allgemeine L¨ osung des statischen Eink¨ orperproblems in der Einsteinschen Gravitationsthe- orie, Arkiv f¨ or matematik, astronomi och fysik, Vol. 16,8 (Almqvist & Wiksell, Stockholm, 1922)

    1922

  5. [5]

    Lemaˆ ıtre, Annales de la Soci´ et´ e Scientifique de Brux- elles53, 51 (1933)

    G. Lemaˆ ıtre, Annales de la Soci´ et´ e Scientifique de Brux- elles53, 51 (1933)

    1933

  6. [6]

    M. A. Javed,Using exceptional points and non Hermitian topology to study fractional charges and apparent event horizons in superconducting circuits., Ph.D. thesis, Uni- versit¨ at zu K¨ oln (2025)

    2025

  7. [7]

    Horstmann, B

    B. Horstmann, B. Reznik, S. Fagnocchi, and J. I. Cirac, Phys. Rev. Lett.104, 250403 (2010)

    2010

  8. [8]

    F. C. Lombardo and G. J. Turiaci, Phys. Rev. D87, 084028 (2013), arXiv:1208.0198 [quant-ph]

    Pith/arXiv arXiv 2013

  9. [9]

    L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Phys. Rev. A63, 023611 (2001)

    2001

  10. [10]

    Steinhauer, Nature Phys.12, 959 (2016), arXiv:1510.00621 [gr-qc]

    J. Steinhauer, Nature Phys.12, 959 (2016), arXiv:1510.00621 [gr-qc]

    Pith/arXiv arXiv 2016

  11. [11]

    Giovanazzi, Phys

    S. Giovanazzi, Phys. Rev. Lett.94, 061302 (2005)

    2005

  12. [12]

    M. P. Blencowe and H. Wang, Philosophical Trans- actions of the Royal Society A: Mathematical, 11 Physical and Engineering Sciences378, 20190224 (2020), https://royalsocietypublishing.org/rsta/article- pdf/doi/10.1098/rsta.2019.0224/1318012/rsta.2019.0224.pdf

    work page doi:10.1098/rsta.2019.0224/1318012/rsta.2019.0224.pdf 2020

  13. [13]

    Sch¨ utzhold and W

    R. Sch¨ utzhold and W. G. Unruh, Phys. Rev. Lett.95, 031301 (2005)

    2005

  14. [14]

    Shiet al., Nature Commun.14, 3263 (2023), arXiv:2111.11092 [quant-ph]

    Y.-H. Shiet al., Nature Commun.14, 3263 (2023), arXiv:2111.11092 [quant-ph]

    arXiv 2023

  15. [15]

    W. G. Unruh and R. Schutzhold, Phys. Rev. D71, 024028 (2005), arXiv:gr-qc/0408009

    Pith/arXiv arXiv 2005

  16. [16]

    Felipe-Elizarraras, H

    R. Felipe-Elizarraras, H. Cruz-Ramirez, K. Garay- Palmett, A. U’Ren, and D. Bermudez, Nature Commu- nications (2026), 10.1038/s41467-026-73812-8

    work page doi:10.1038/s41467-026-73812-8 2026

  17. [17]

    Drori, Y

    J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, and U. Leonhardt, Physical Review Letters122(2019), 10.1103/PhysRevLett.122.010404

    work page doi:10.1103/physrevlett.122.010404 2019

  18. [18]

    Falque, A

    K. Falque, A. Delhom, Q. Glorieux, E. Giacobino, A. Bramati, and M. J. Jacquet, Phys. Rev. Lett.135, 023401 (2025)

    2025

  19. [19]

    P. D. Nation, J. R. Johansson, M. P. Blencowe, and F. Nori, Rev. Mod. Phys.84, 1 (2012)

    2012

  20. [20]

    Ferreri and F

    A. Ferreri and F. K. Wilhelm, Phys. Rev. Applied23, 024026 (2025), arXiv:2403.08508 [quant-ph]

    arXiv 2025

  21. [21]

    Ferreri, D

    A. Ferreri, D. E. Bruschi, and F. K. Wilhelm, Phys. Rev. Res.6, 033204 (2024), arXiv:2401.16976 [quant-ph]

    arXiv 2024

  22. [22]

    C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Nature479, 376 (2011), arXiv:1105.4714 [quant-ph]

    Pith/arXiv arXiv 2011

  23. [23]

    Unruh and R

    W. Unruh and R. Schuetzhold,Quantum analogues. From phase transitions to black holes and cosmology, Vol. 718 (Springer, 2007)

    2007

  24. [24]

    F. C. Lombardo and G. J. Turiaci, Phys. Rev. Lett.108, 261301 (2012)

    2012

  25. [25]

    P. D. Nation, M. P. Blencowe, A. J. Rimberg, and E. Buks, Phys. Rev. Lett.103, 087004 (2009)

    2009

  26. [26]

    Katayama, N

    H. Katayama, N. Hatakenaka, T. Fujii, and M. P. Blencowe, Phys. Rev. Res.5, L022055 (2023)

    2023

  27. [27]

    Robertson, J

    S. Robertson, J. Phys. B: At. Mol. Opt. Phys. 45 (2012)

    2012

  28. [28]

    Damour and R

    T. Damour and R. Ruffini, Phys. Rev. D14, 332 (1976)

    1976

  29. [29]

    Brout, S

    R. Brout, S. Massar, R. Parentani, and P. Spindel, Phys. Rept.260, 329 (1995), arXiv:0710.4345 [gr-qc]

    Pith/arXiv arXiv 1995

  30. [30]

    Brout, S

    R. Brout, S. Massar, R. Parentani, and P. Spindel, Phys. Rev. D52, 4559 (1995), arXiv:hep-th/9506121

    Pith/arXiv arXiv 1995

  31. [31]

    N. E. Frattini, U. Vool, S. Shankar, A. Narla, K. M. Sliwa, and M. H. Devoret, Appl. Phys. Lett.110, 222603 (2017), arXiv:1702.00869 [cond-mat.supr-con]

    Pith/arXiv arXiv 2017

  32. [32]

    Taniuti, Progress of Theoretical Physics Supplement 55, 1 (1974), https://academic.oup.com/ptps/article- pdf/doi/10.1143/PTPS.55.1/5391622/55-1.pdf

    T. Taniuti, Progress of Theoretical Physics Supplement 55, 1 (1974), https://academic.oup.com/ptps/article- pdf/doi/10.1143/PTPS.55.1/5391622/55-1.pdf

    work page doi:10.1143/ptps.55.1/5391622/55-1.pdf 1974

  33. [33]

    C. S. Gardner and G. K. Morikawa,Similarity in the asymptotic behavior of collission-free hydromagnetic waves and water waves, Tech. Rep. (New York Univ., New York. Inst. of Mathematical Sciences, 1960)

    1960

  34. [34]

    Tian and J

    Z. Tian and J. Du, Eur. Phys. J. C79, 994 (2019), arXiv:1808.03125 [quant-ph]

    arXiv 2019

  35. [35]

    Petruccione and H.-P

    F. Petruccione and H.-P. Breuer,The Theory of Open Quantum Systems(Oxford University Press, 2007)

    2007

  36. [36]

    P. C. Davies, Reports on Progress in Physics41, 1313 (1978)

    1978

  37. [37]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Rev. Mod. Phys.93, 025005 (2021), arXiv:2005.12667 [quant-ph]

    arXiv 2021

  38. [38]

    N. F. Del Grosso, R. G. Corti˜ nas, P. I. Villar, F. C. Lom- bardo, and J. P. Paz, Phys. Rev. A111, 042606 (2025)

    2025

  39. [39]

    Tr´ avn´ ıˇ cek, K

    V. Tr´ avn´ ıˇ cek, K. Bartkiewicz, A.ˇCernoch, and K. Lemr, Phys. Rev. Lett.123, 260501 (2019), arXiv:1907.02292 [quant-ph]

    arXiv 2019