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arxiv: 2605.21628 · v1 · pith:F7FBUHAQnew · submitted 2026-05-20 · 🪐 quant-ph · cond-mat.stat-mech· math-ph· math.MP· nlin.CD

What We Talk About When We Talk About Dissipative Quantum Chaos

Lucas S\'a , Pedro Ribeiro , Sergey Denisov This is my paper

Pith reviewed 2026-05-22 09:14 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechmath-phmath.MPnlin.CD
keywords dissipative quantum chaosopen quantum systemsLiouvillian spectrumquantum integrabilitylevel statisticsopen-system dynamicschaos diagnostics
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The pith

Dissipative quantum chaos defines chaotic open systems through the spectral statistics of the Liouvillian superoperator that governs their evolution.

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

The paper reviews how ideas from conventional quantum chaos in isolated systems extend to open quantum systems that lose energy or coherence to their surroundings. It argues that the spectrum of the Liouvillian, the operator describing density-matrix evolution, supplies the necessary tools to identify chaotic behavior and measure its strength in these dissipative cases. Foundations date to the late 1980s, with renewed activity and first experiments in the last decade. If correct, the approach supplies concrete diagnostics that work even when the system continuously exchanges information with an environment. This matters for realistic quantum devices where perfect isolation is impossible.

Core claim

Dissipative quantum chaos extends the methodology of Hamiltonian quantum chaos to open quantum dynamics by basing distinction between chaotic and integrable open systems on the spectral properties of the Liouvillian and related operators that govern their evolution. The review covers the initial proposals from the late 1980s, the subsequent quiet period, and the strong recent growth in theoretical and experimental work that tests these spectral criteria.

What carries the argument

The Liouvillian superoperator whose complex eigenvalues and level statistics are proposed to serve as the diagnostic for chaotic versus integrable open-system behavior.

If this is right

  • Open quantum systems become classifiable as chaotic or integrable using the same spectral tools applied to closed systems.
  • Quantitative measures of chaoticity become available for dynamics that include dissipation and decoherence.
  • Experimental tests of spectral predictions are now feasible in platforms with controlled loss.
  • The framework supplies diagnostics for quantum devices that cannot be perfectly isolated.

Where Pith is reading between the lines

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

  • The same spectral approach might link dissipative quantum chaos to classical chaotic attractors in driven-dissipative systems.
  • Level statistics of the Liouvillian could serve as a practical benchmark for quantum simulators that include engineered dissipation.
  • If the spectral criterion holds, it would allow systematic comparison of chaoticity across different open-system models without requiring full time evolution.

Load-bearing premise

That the spectral features of the Liouvillian or similar generators provide a sufficient and complete basis for defining and quantifying dissipative quantum chaos.

What would settle it

Observation of an open quantum system whose long-time dynamics shows clear signatures of chaos yet whose Liouvillian spectrum lacks the expected level repulsion or other chaotic statistics.

Figures

Figures reproduced from arXiv: 2605.21628 by Lucas S\'a, Pedro Ribeiro, Sergey Denisov.

Figure 1
Figure 1. Figure 1: This idea was proposed in Ref. [49]. It was then tested with a model that describes an open, periodically driven Kerr cavity [33]. In [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
read the original abstract

Dissipative quantum chaos is an emerging theory that is expected to extend the ideas, concepts, and methodology of conventional Hamiltonian quantum chaos from coherent evolution to open quantum dynamics. The new theory should provide a set of tools to distinguish chaotic open quantum systems from integrable ones, as well as quantitative measures of their chaoticity (or, conversely, integrability). The foundations of this theory were laid in the late 1980s, and from the very start it was clear that, like its Hamiltonian predecessor, it had to be based on the spectral properties of the operators governing open quantum evolution. After these first steps, the field remained relatively quiet for many years and it is only over the last decade that the development of dissipative quantum chaos has received a strong boost, as confirmed by a large number of publications on this topic and, very recently, the first experiments performed to test its theoretical predictions. In this chapter, we review these recent developments and outline the basic foundations of dissipative quantum chaos.

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

1 major / 1 minor

Summary. This review chapter traces the development of dissipative quantum chaos from its late-1980s foundations to recent theoretical and experimental progress. It claims that, like Hamiltonian quantum chaos, dissipative quantum chaos must be diagnosed via the spectral properties of the operators (primarily the Liouvillian) that govern open-system evolution, thereby furnishing tools to distinguish chaotic from integrable open quantum systems and to quantify their degree of chaoticity.

Significance. If the review faithfully represents the cited literature, it offers a useful consolidation of an emerging subfield at a moment when the first experiments are appearing. The explicit linkage between complex-plane spectral statistics and open-system diagnostics, together with the mention of recent experimental tests, supplies a reference point that could help standardize terminology and guide quantitative studies of dissipative many-body dynamics.

major comments (1)
  1. [Abstract / Introduction] Abstract and opening paragraphs: the assertion that dissipative quantum chaos 'had to be based on the spectral properties of the operators governing open quantum evolution' is presented as self-evident from the late-1980s literature. Because the Liouvillian is non-normal, its spectrum lies in the complex plane and admits Jordan blocks and exceptional points whose relation to conventional level-spacing or spectral-form-factor diagnostics is not automatic. The review should explicitly discuss whether these additional structures can produce Poisson-like statistics in known chaotic models or GOE-like statistics in integrable ones; without such discussion the foundational claim remains under-supported.
minor comments (1)
  1. [Abstract] The phrase 'a large number of publications' is used without a quantitative citation count or a curated reference list of the most influential recent works; adding either would increase the review's utility as a field guide.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for providing constructive feedback. We address the major comment in detail below and have made revisions to strengthen the presentation of the foundational claims.

read point-by-point responses

  1. Referee: [Abstract / Introduction] Abstract and opening paragraphs: the assertion that dissipative quantum chaos 'had to be based on the spectral properties of the operators governing open quantum evolution' is presented as self-evident from the late-1980s literature. Because the Liouvillian is non-normal, its spectrum lies in the complex plane and admits Jordan blocks and exceptional points whose relation to conventional level-spacing or spectral-form-factor diagnostics is not automatic. The review should explicitly discuss whether these additional structures can produce Poisson-like statistics in known chaotic models or GOE-like statistics in integrable ones; without such discussion the foundational claim remains under-supported.

    Authors: We appreciate the referee highlighting the importance of addressing the non-normality of the Liouvillian and its consequences for spectral diagnostics. The late-1980s works, such as those by Grobe et al. and others, did indeed propose using spectral properties of the Liouvillian for characterizing dissipative chaos, even while recognizing its non-Hermitian nature. To make this more explicit and to support the claim, we have revised the introduction to include a dedicated paragraph discussing the spectrum in the complex plane, the role of exceptional points, and Jordan blocks. We note that while these features can lead to non-trivial eigenvalue distributions, established diagnostics in the literature, including the use of complex-plane level spacing ratios and the spectral form factor adapted for non-normal operators, have been shown to distinguish chaotic from integrable behavior in various models. We cite recent works that investigate these aspects and clarify that, in known chaotic dissipative systems, the statistics do not reduce to Poisson-like despite the presence of such structures. We acknowledge that a exhaustive study of all possible counterexamples is an ongoing research topic, but the review now provides a clearer foundation for the claim. revision: yes

Circularity Check

0 steps flagged

Review paper cites external foundations with no internal circular derivations

full rationale

This is a review chapter that summarizes historical foundations from the late 1980s and recent literature on dissipative quantum chaos without presenting original derivations, fitted parameters, or new predictions. The claim that the theory 'had to be based on the spectral properties of the operators governing open quantum evolution' is attributed to prior external work rather than derived or fitted within the paper itself. No equations or results reduce by construction to the paper's own inputs, self-citations are not load-bearing for any central claim, and the analysis remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper; no new free parameters, axioms, or invented entities are introduced by the authors themselves.

pith-pipeline@v0.9.0 · 5714 in / 1023 out tokens · 26592 ms · 2026-05-22T09:14:12.482552+00:00 · methodology

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Works this paper leans on

175 extracted references · 175 canonical work pages · 5 internal anchors

  1. [1]

    Eckmann and D

    J.-P . Eckmann and D. Ruelle,Ergodic theory of chaos and strange attractors,Reviews of Modern Physics57(1985) 617

    work page 1985

  2. [2]

    Lichtenberg and M.A

    A.J. Lichtenberg and M.A. Lieberman,Regular and Chaotic Dynamics, Springer-Verlag, New Y ork, 2 ed. (1992)

    work page 1992

  3. [3]

    Ott,Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 2 ed

    E. Ott,Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 2 ed. (2002)

    work page 2002

  4. [4]

    Toda and K

    M. Toda and K. Ikeda,Quantal Lyapunov exponent,Physics Letters A124(1987) 165

    work page 1987

  5. [5]

    Haake, H

    F . Haake, H. Wiedemann and K. ˙Zyczkowski,Lyapunov exponents from quantum dynamics,Annalen der Physik1(1992) 531

    work page 1992

  6. [6]

    ˙Zyczkowski and W

    K. ˙Zyczkowski and W. Słomczy´nski,How to generalize the Lapunov exponent for quantum mechanics,Vistas in Astronomy37(1993)

    work page 1993

  7. [7]

    Casati, B.V

    G. Casati, B.V. Chirikov, F .M. Izrailev and J. Ford,Stochastic behavior of a quantum pendulum under a periodic perturbation, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, G. Casati and J. Ford, eds., vol. 93 ofLecture Notes in Physics, (Berlin, Heidelberg), pp. 334–352, Springer (1979)

    work page 1979

  8. [8]

    Haake, M

    F . Haake, M. Ku´s and R. Scharf,Classical and quantum chaos for a kicked top,Zeitschrift f ¨ur Physik B Condensed Matter65(1987) 381

    work page 1987

  9. [9]

    Emary and T

    C. Emary and T. Brandes,Chaos and the quantum phase transition in the Dicke model,Physical Review E67(2003) 066203

    work page 2003

  10. [10]

    Berry,Semi-classical mechanics in phase space: A study of wigner’s function,Philosophical Transactions of the Royal Society of London A287(1977) 237

    M.V. Berry,Semi-classical mechanics in phase space: A study of wigner’s function,Philosophical Transactions of the Royal Society of London A287(1977) 237

    work page 1977

  11. [11]

    Balazs and B.K

    N.L. Balazs and B.K. Jennings,Wigner’s function and other distribution functions in fock phase spaces,Physics Reports104(1984) 347

    work page 1984

  12. [12]

    Takahashi,Wigner and Husimi functions in quantum mechanics,Journal of the Physical Society of Japan55(1986) 762

    K. Takahashi,Wigner and Husimi functions in quantum mechanics,Journal of the Physical Society of Japan55(1986) 762

    work page 1986

  13. [13]

    St ¨ockmann,Quantum Chaos: An Introduction, Cambridge University Press, Cambridge (1999), 10.1017/CBO9780511524622

    H.-J. St ¨ockmann,Quantum Chaos: An Introduction, Cambridge University Press, Cambridge (1999), 10.1017/CBO9780511524622

    work page doi:10.1017/cbo9780511524622 1999

  14. [14]

    Haake,Quantum Signatures of Chaos, Springer Series in Synergetics Ser, Springer, Cham, 4th ed ed

    F . Haake,Quantum Signatures of Chaos, Springer Series in Synergetics Ser, Springer, Cham, 4th ed ed. (2019)

    work page 2019

  15. [15]

    Jensen,Quantum chaos,Nature355(1992) 311

    R.V. Jensen,Quantum chaos,Nature355(1992) 311

    work page 1992

  16. [16]

    W. Zhou, Z. Chen, B. Zhang, C.H. Yu, W. Lu and S.C. Shen,Magnetic field control of the quantum chaotic dynamics of highly excited rovibrational states of ultracold molecules,Physical Review Letters105(2010) 024101

    work page 2010

  17. [17]

    Khlebnikov, D.A

    V.A. Khlebnikov, D.A. Pershin, V.V. Tsyganok, E.T. Davletov, I.S. Cojocaru, E.S. Fedorova et al.,Random to chaotic statistic transformation in low-field Fano-Feshbach resonances of cold thulium atoms,Physical Review Letters123(2019) 213402

    work page 2019

  18. [18]

    Roushan, C

    P . Roushan, C. Neill, J. Tangpanitanon, V.M. Bastidas, A. Megrant, R. Barends et al.,Spectroscopic signatures of localization with interacting photons in superconducting qubits,Science358(2017) 1175

    work page 2017

  19. [19]

    Landi, D

    G.T. Landi, D. Poletti and G. Schaller,Nonequilibrium boundary-driven quantum systems: Models, methods, and properties,Reviews of Modern Physics94(2022) 045006

    work page 2022

  20. [20]

    Sieberer, M

    L.M. Sieberer, M. Buchhold, J. Marino and S. Diehl,Universality in driven open quantum matter,Reviews of Modern Physics97(2025) 025004

    work page 2025

  21. [21]

    Khoruzhenko and H.-J

    B.A. Khoruzhenko and H.-J. Sommers,Non-Hermitian random matrix ensembles, inThe Oxford Handbook of Random Matrix Theory, G. Akemann, J. Baik and P .D. Francesco, eds., (Oxford), pp. 376–397, Oxford University Press (2011)

    work page 2011

  22. [22]

    Bernard and A

    D. Bernard and A. LeClair,A classification of non-Hermitian random matrices, inStatistical Field Theories, A. Cappelli and G. Mussardo, eds., (Dordrecht), pp. 207–214, Springer (2002), https://link.springer.com/chapter/10.1007/978-94-010-0514-2 19

    work page doi:10.1007/978-94-010-0514-2 2002

  23. [23]

    Magnea,Random matrices beyond the Cartan classification,J

    U. Magnea,Random matrices beyond the Cartan classification,J. Phys. A41(2008) 045203

    work page 2008

  24. [24]

    Free probability and random matri- ces

    J.A. Mingo and R. Speicher,Free Probability and Random Matrices, vol. 35 ofFields Institute Monographs, Springer, New Y ork (2017), 10.1007/978-1-4939-6942-5

    work page doi:10.1007/978-1-4939-6942-5 2017

  25. [25]

    Breuer and F

    H.-P . Breuer and F . Petruccione,The Theory of Open Quantum Systems, Clarendon Press, Oxford, repr ed. (2010)

    work page 2010

  26. [26]

    Quantum Computing in the NISQ era and beyond

    J. Preskill,Quantum computing in the NISQ era and beyond,Quantum2(2018) 79 [1801.00862]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [27]

    Sommer, F

    O.E. Sommer, F . Piazza and D.J. Luitz,Many-body hierarchy of dissipative timescales in a quantum computer,Phys. Rev. Res.3(2021) 023190

    work page 2021

  28. [28]

    K. Wold, P . Ribeiro and S. Denisov,Spectra of noisy parameterized quantum circuits: Single-Ring universality, July, 2025. 10.48550/arXiv.2405.11625

    work page doi:10.48550/arxiv.2405.11625 2025

  29. [29]

    K. Wold, Z. Zhu, F . Jin, X. Zhu, Z. Bao, J. Zhong et al.,Experimental detection of dissipative quantum chaos,arXiv preprint arXiv:2506.04325(2025)

    work page arXiv 2025

  30. [30]

    Quantum channels & operations: Guided tour

    M.M. Wolf, “Quantum channels & operations: Guided tour.” Lecture notes, 2012

    work page 2012

  31. [31]

    Esposito, U

    M. Esposito, U. Harbola and S. Mukamel,Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Reviews of Modern Physics81(2009) 1665

    work page 2009

  32. [32]

    Ferrari, L

    F . Ferrari, L. Gravina, D. Eeltink, P . Scarlino, V. Savona and F . Minganti,Dissipative quantum chaos unveiled by stochastic quantum trajectories,Physical Review Research7(2025) 013276

    work page 2025

  33. [33]

    Yusipov, O.S

    I.I. Yusipov, O.S. Vershinina, S.V. Denisov and M.V. Ivanchenko,Photon waiting-time distributions: A keyhole into dissipative quantum chaos,Chaos30(2020) 023107

    work page 2020

  34. [34]

    Pankratov, A.V

    A.L. Pankratov, A.V. Gordeeva, A.V. Chiginev, L.S. Revin, A.V. Blagodatkin, N. Crescini et al.,Detection of single-mode thermal microwave photons using an underdamped josephson junction,Nature Communications16(2025) 3457

    work page 2025

  35. [35]

    Gorini, A

    V. Gorini, A. Kossakowski and E.C.G. Sudarshan,Completely positive dynamical semigroups of N-level systems,Journal of Mathematical Physics17(1976) 821

    work page 1976

  36. [36]

    Lindblad,On the generators of quantum dynamical semigroups,Communications in Mathematical Physics48(1976) 119

    G. Lindblad,On the generators of quantum dynamical semigroups,Communications in Mathematical Physics48(1976) 119

    work page 1976

  37. [37]

    Wiseman and G.J

    H.M. Wiseman and G.J. Milburn,Quantum Measurement and Control, Cambridge University Press, Cambridge, UK New Y ork (2010)

    work page 2010

  38. [38]

    M.M. Wolf, J. Eisert, T.S. Cubitt and J.I. Cirac,Assessing non-Markovian quantum dynamics,Physical Review Letters101(2008) 150402

    work page 2008

  39. [39]

    Grobe, F

    R. Grobe, F . Haake and H.-J. Sommers,Quantum distinction of regular and chaotic dissipative motion,Physical Review Letters61 (1988) 1899

    work page 1988

  40. [40]

    Akemann, M

    G. Akemann, M. Kieburg, A. Mielke and T. Prosen,Universal signature from integrability to chaos in dissipative open quantum systems, Phys. Rev. Lett.123(2019) 254101

    work page 2019

  41. [41]

    Dahan, G

    D. Dahan, G. Arwas and E. Grosfeld,Classical and quantum chaos in chirally-driven, dissipative Bose-Hubbard systems,npj Quantum Information8(2022) 14

    work page 2022

  42. [42]

    Pereira, N.S.S

    R.M.C. Pereira, N.S.S. de Buruaga, K. Wold, L. S ´a, S. Denisov and P . Ribeiro,Dissipation-induced threshold on integrability footprints, Apr., 2025. 10.48550/arXiv.2504.10255

    work page doi:10.48550/arxiv.2504.10255 2025

  43. [43]

    Ferrari, V

    F . Ferrari, V. Savona and F . Minganti,Chaos and thermalization in open quantum systems, 2025. 10.48550/ARXIV.2505.18260

    work page doi:10.48550/arxiv.2505.18260 2025

  44. [44]

    Prosen and M

    T. Prosen and M. ˇZnidariˇc,Eigenvalue statistics as an indicator of integrability of nonequilibrium density operators,Physical Review Letters111(2013) 124101

    work page 2013

  45. [45]

    Richter, L

    J. Richter, L. S ´a and M. Haque,Integrability versus chaos in the steady state of many-body open quantum systems,Phys. Rev. E111 24What We Talk About When We Talk About Dissipative Quantum Chaos (2025) 064103

    work page 2025

  46. [46]

    Villase ˜nor, L.F

    D. Villase ˜nor, L.F . Santos and P . Barberis-Blostein,Breakdown of the quantum distinction of regular and chaotic classical dynamics in dissipative systems,Physical Review Letters133(2024) 240404

    work page 2024

  47. [47]

    G. Rufo, S. Rufo, P . Ribeiro and S. Chesi,Quantum and semi-classical signatures of dissipative chaos in the steady state, 2025. 10.48550/ARXIV.2506.14961

    work page doi:10.48550/arxiv.2506.14961 2025

  48. [49]

    Yusipov, O.S

    I.I. Yusipov, O.S. Vershinina, S.V. Denisov, S.P . Kuznetsov and M.V. Ivanchenko,Quantum Lyapunov exponents beyond continuous measurements,Chaos: An Interdisciplinary Journal of Nonlinear Science29(2019) 063130

    work page 2019

  49. [50]

    Complexity of Quantum Trajectories

    L. Lumia, E. Tirrito, M. Collura, F .H.L. Essler and R. Fazio,Complexity of quantum trajectories, 2026. 10.48550/arXiv.2602.00232

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2602.00232 2026

  50. [51]

    Oraevskii,Masers, lasers, and strange attractors,Soviet Journal of Quantum Electronics11(1981) 71

    A.N. Oraevskii,Masers, lasers, and strange attractors,Soviet Journal of Quantum Electronics11(1981) 71

    work page 1981

  51. [52]

    Graham,Quantization of a two-dimensional map with a strange attractor,Physics Letters A99(1983) 131

    R. Graham,Quantization of a two-dimensional map with a strange attractor,Physics Letters A99(1983) 131

    work page 1983

  52. [53]

    Graham,Quantum noise and strange attractors,Physics Reports103(1984) 143

    R. Graham,Quantum noise and strange attractors,Physics Reports103(1984) 143

    work page 1984

  53. [54]

    Graham,Global and local dissipation in a quantum map,Zeitschrift f ¨ur Physik B Condensed Matter59(1985) 75

    R. Graham,Global and local dissipation in a quantum map,Zeitschrift f ¨ur Physik B Condensed Matter59(1985) 75

    work page 1985

  54. [55]

    Elgin and S

    J.N. Elgin and S. Sarkar,Quantum fluctuations and the Lorenz strange attractor,Physical Review Letters52(1984) 1215

    work page 1984

  55. [56]

    quantum fluctuations and the Lorenz strange attractor

    R. Graham,Comment on “quantum fluctuations and the Lorenz strange attractor”,Physical Review Letters53(1984) 1506

    work page 1984

  56. [57]

    Bu ˇca, J

    B. Bu ˇca, J. Tindall and D. Jaksch,Non-stationary coherent quantum many-body dynamics through dissipation,Nature Communications 10(2019) 1730

    work page 2019

  57. [58]

    Dittrich and R

    T. Dittrich and R. Graham,Quantization of the kicked rotator with dissipation,Zeitschrift f ¨ur Physik B Condensed Matter62(1986) 515

    work page 1986

  58. [59]

    Naves, T.K

    C.B. Naves, T.K. Kvorning and J. Larson,When level repulsion fails: Non-normality and chaos in open quantum systems, 2026

    work page 2026

  59. [60]

    Grobe and F

    R. Grobe and F . Haake,Universality of cubic-level repulsion for dissipative quantum chaos,Physical Review Letters62(1989) 2893

    work page 1989

  60. [61]

    Braun, Dissipative Quantum Chaos and Decoherence, Springer Tracts in Modern Physics, Springer Berlin Heidelberg, 2003

    D. Braun,Dissipative Quantum Chaos and Decoherence, vol. 172 ofSpringer Tracts in Modern Physics, Springer, Berlin, Heidelberg (2001), 10.1007/3-540-40916-5

    work page doi:10.1007/3-540-40916-5 2001

  61. [62]

    Bruzda, V

    W. Bruzda, V. Cappellini, H.-J. Sommers and K. ˙Zyczkowski,Random quantum operations,Physics Letters A373(2009) 320

    work page 2009

  62. [63]

    Lange and C

    S. Lange and C. Timm,Random-matrix theory for the Lindblad master equation,Chaos: An Interdisciplinary Journal of Nonlinear Science31(2021) 023101

    work page 2021

  63. [64]

    Can,Random Lindblad dynamics,J

    T. Can,Random Lindblad dynamics,J. Phys. A52(2019) 485302

    work page 2019

  64. [65]

    T. Can, V. Oganesyan, D. Orgad and S. Gopalakrishnan,Spectral gaps and midgap states in random quantum master equations, Physical Review Letters123(2019) 234103

    work page 2019

  65. [66]

    L. S ´a, P . Ribeiro and T. Prosen,Spectral and steady-state properties of random liouvillians,Journal of Physics A: Mathematical and Theoretical53(2020) 305303

    work page 2020

  66. [67]

    L. S ´a, P . Ribeiro and T. Prosen,Complex Spacing Ratios: A signature of dissipative quantum chaos,Physical Review X10(2020) 021019

    work page 2020

  67. [68]

    Mehta,Random matrices, Elsevier, New Y ork (2004)

    M.L. Mehta,Random matrices, Elsevier, New Y ork (2004)

    work page 2004

  68. [69]

    Denisov, T

    S. Denisov, T. Laptyeva, W. Tarnowski, D. Chru´sci´nski and K. ˙Zyczkowski,Universal spectra of random Lindblad operators,Physical Review Letters123(2019) 140403

    work page 2019

  69. [70]

    Gradshteyn and I.M

    I.S. Gradshteyn and I.M. Ryzhik,Table of Integrals, Series, and Products, Academic Press, Amsterdam, 7 ed. (2007)

    work page 2007

  70. [71]

    Tarnowski,Real spectra of large real asymmetric random matrices,Physical Review E105(2022) L012104

    W. Tarnowski,Real spectra of large real asymmetric random matrices,Physical Review E105(2022) L012104

    work page 2022

  71. [72]

    in preparation

    M. Hontarenko, W. Tarnowski, S. Denisov and K. ˙Zyczkowski, “in preparation.” 2026

    work page 2026

  72. [73]

    L. S ´a, P . Ribeiro, T. Can and T. Prosen,Spectral transitions and universal steady states in random Kraus maps and circuits,Physical Review B102(2020) 134310

    work page 2020

  73. [74]

    Poulin,Lieb-Robinson bound and locality for general Markovian quantum dynamics,Physical Review Letters104(2010) 190401

    D. Poulin,Lieb-Robinson bound and locality for general Markovian quantum dynamics,Physical Review Letters104(2010) 190401

    work page 2010

  74. [75]

    Samos, R

    N. Samos, R. Bistro ´n, M. Rudzi´nski, R.M.C. Pereira, K. ˙Zyczkowski and P . Ribeiro,Fidelity decay and error accumulation in random quantum circuits,SciPost Physics19(2025) 013

    work page 2025

  75. [76]

    Matsoukas-Roubeas, T

    A.S. Matsoukas-Roubeas, T. Prosen and A.D. Campo,Quantum chaos and coherence: Random parametric quantum channels, Quantum8(2024) 1446

    work page 2024

  76. [77]

    L. S ´a, P . Ribeiro and T. Prosen,Integrable nonunitary open quantum circuits,Physical Review B103(2021) 115132

    work page 2021

  77. [78]

    Su and I

    L. Su and I. Martin,Integrable nonunitary quantum circuits,Phys. Rev. B106(2022) 134312

    work page 2022

  78. [79]

    Oganesyan and D.A

    V. Oganesyan and D.A. Huse,Localization of interacting fermions at high temperature,Physical Review B75(2007) 155111

    work page 2007

  79. [80]

    Y .Y . Atas, E. Bogomolny, O. Giraud and G. Roux,Distribution of the ratio of consecutive level spacings in random matrix ensembles, Physical Review Letters110(2013) 084101

    work page 2013

  80. [81]

    Markum, R

    H. Markum, R. Pullirsch and T. Wettig,Non-Hermitian random matrix theory and lattice QCD with chemical potential,Physical Review Letters83(1999) 484

    work page 1999

Showing first 80 references.