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Boundary-Controlled Liouvillian Relaxation with Exact Steady States Fixed by Dissipative Disorder

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Pith's one-line read Boundary conditions control relaxation without changing the reduced steady state in disordered dissipative chains.

desk verdict The paper gives a concrete construction for using cyclic boundaries to speed relaxation while keeping the same reduced steady-state occupations fixed by dissipative disorder, but the gauge single-valuedness on the cycle is the key point to check. read the letter →

arxiv 2606.22065 v2 pith:CWT3VX7M submitted 2026-06-20 cond-mat.dis-nn

Yazhuang Miao , Weizh Ma , Yong Wang , Xiaolong Zhao , Xuexi Yi This is my paper · ORCID
classification cond-mat.dis-nn
keywords boundaryconditionsLiouvillianrelaxationdissipativedisordersteadystatesquantumlinkchaingaugetransformationdynamics
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

In open quantum lattice systems, changing the boundary condition would appear to alter both the steady state and the nonzero Liouvillian spectrum. The paper shows that in a disordered dissipative quantum link chain, an accumulated field defined by link-resolved dissipative disorder fixes the steady state. A gauge-generated transformation built from this field produces exact symmetry-resolved steady states whose reduced matter occupations depend on the accumulated field but remain unchanged by the boundary choice. A reciprocal cyclic boundary condition is constructed that preserves these occupations while modifying the nonzero Liouvillian spectrum, so open and cyclic chains reach the same reduced matter steady-occupation profile but with different Liouvillian gaps. The cyclic closure accelerates relaxation, and in the strong-dissipation limit the difference reduces to a spectral comparison of effective exclusion processes with open versus cyclic boundaries.

What carries the argument

Gauge-generated transformation built from the accumulated field defined by link-resolved dissipative disorder, which yields exact symmetry-resolved steady states with boundary-independent reduced matter occupations.

What would settle it

Numerical simulation or measurement of the reduced matter occupations in the steady state of a small disordered dissipative quantum link chain under both open and reciprocal cyclic boundary conditions; mismatch between the two would falsify the claim.

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Extended reading notes

Core claim

Boundary conditions can be used to control relaxation without changing the reduced steady state. In a disordered dissipative quantum link chain, the steady state is determined by an accumulated field defined by link-resolved dissipative disorder, and a gauge-generated transformation built from this field gives exact symmetry-resolved steady states with nonuniform, accumulated-field-dependent reduced matter occupations. A reciprocal cyclic boundary condition preserves these matter occupations while changing the nonzero Liouvillian spectrum. Consequently, open and cyclic chains relax to the same reduced matter steady-occupation profile with different Liouvillian gaps, with the cyclic closure a

Load-bearing premise

The gauge-generated transformation built from the accumulated field defined by link-resolved dissipative disorder produces exact symmetry-resolved steady states whose reduced matter occupations are independent of the choice between open and reciprocal cyclic boundaries.

Editorial extensions

If this is right

  • Open and cyclic chains reach identical reduced matter steady-occupation profiles.
  • The cyclic boundary changes the nonzero Liouvillian spectrum and accelerates relaxation.
  • In the strong-dissipation limit the relaxation difference reduces to a spectral comparison of effective exclusion processes with open versus cyclic boundaries.

Reading between the lines

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

  • Boundary engineering could allow independent tuning of relaxation speed in other open quantum systems where disorder fixes the steady state.
  • The separation of steady-state control from dynamical spectrum may extend to classical stochastic processes or nonequilibrium many-body models.
  • Similar gauge constructions might apply to systems with other forms of link disorder to fix target states while adjusting convergence rates.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The manuscript claims that in a disordered dissipative quantum link chain, the steady state is fixed by an accumulated field from link-resolved dissipative disorder. A gauge-generated transformation yields exact symmetry-resolved steady states with nonuniform, accumulated-field-dependent reduced matter occupations. A reciprocal cyclic boundary condition is then constructed that preserves these matter occupations while altering the nonzero Liouvillian spectrum, so that open and cyclic chains reach the same reduced steady-occupation profile but with different gaps (cyclic accelerating relaxation). In the strong-dissipation limit the difference reduces to a spectral comparison between effective exclusion processes with open versus cyclic boundaries.

Significance. If the central construction holds, the result is significant because it isolates boundary engineering as a means to tune Liouvillian gaps independently of the reduced steady state in a disordered open quantum system. The exact gauge transformation providing symmetry-resolved steady states and the explicit strong-dissipation mapping to exclusion-process spectra are concrete strengths that make the acceleration claim falsifiable and potentially useful for dissipative state preparation.

major comments (1)
  1. [gauge transformation and cyclic-boundary construction] The construction of the reciprocal cyclic boundary condition (described after the gauge transformation) must explicitly verify single-valuedness of the gauge on the cycle. For generic accumulated fields the total winding must satisfy a quantization condition; if the closing link is chosen to enforce this without modifying the cumulative profile seen by the matter degrees of freedom, the reduced occupations remain boundary-independent. The manuscript should supply the explicit condition or the choice rule for the closing link, as this is load-bearing for the claim that the reduced steady state is unchanged.
minor comments (1)
  1. The term 'reciprocal' cyclic boundary condition is used without a one-sentence definition or reference; adding this would improve readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the gauge transformation and cyclic-boundary construction. We address the point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [gauge transformation and cyclic-boundary construction] The construction of the reciprocal cyclic boundary condition (described after the gauge transformation) must explicitly verify single-valuedness of the gauge on the cycle. For generic accumulated fields the total winding must satisfy a quantization condition; if the closing link is chosen to enforce this without modifying the cumulative profile seen by the matter degrees of freedom, the reduced occupations remain boundary-independent. The manuscript should supply the explicit condition or the choice rule for the closing link, as this is load-bearing for the claim that the reduced steady state is unchanged.

    Authors: We agree that an explicit verification of single-valuedness is required for rigor. In the construction, the reciprocal cyclic boundary condition is obtained by choosing the dissipative disorder strength on the closing link so that the total accumulated field around the cycle equals an integer multiple of the gauge period (2π in the units of the model). This quantization condition is enforced by the boundary link alone and does not alter the cumulative field profile experienced by the matter sites, thereby leaving the reduced steady-state occupations unchanged. We will add a new paragraph immediately after the definition of the cyclic boundary condition that states the quantization requirement, derives the explicit choice rule for the closing-link parameter, and confirms that the gauge remains single-valued while the matter occupations are preserved. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in the derivation chain

full rationale

The paper defines an accumulated field from the link-resolved dissipative disorder and constructs a gauge transformation from it to obtain exact symmetry-resolved steady states for the open chain. It then explicitly constructs a reciprocal cyclic boundary condition that preserves the reduced matter occupations (by design of the closure) while altering the nonzero Liouvillian spectrum. The central claim—that open and cyclic chains share the same reduced steady-occupation profile but differ in relaxation rate—is therefore shown by direct construction rather than by any reduction of a prediction to a fitted input, self-citation chain, or definitional equivalence. No load-bearing step in the abstract or described derivation invokes prior self-citations, uniqueness theorems from the same authors, or ansatzes smuggled via citation; the result remains self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 0 assumptions · 1 invented entities

Abstract-only review; the model implicitly relies on the standard Lindblad master equation for open quantum systems and on the existence of a well-defined accumulated field from link disorder, but no explicit free parameters, axioms, or invented entities beyond the field itself are stated.

invented entities (1)
  • accumulated field
    purpose: Encodes the link-resolved dissipative disorder that fixes the reduced steady-state occupations
    Introduced in the abstract as the quantity that determines the steady state independently of boundary choice

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Cite this review

Pith. "Pith review of Boundary-Controlled Liouvillian Relaxation with Exact Steady States Fixed by Dissipative Disorder." pith.science (2026). https://pith.science/paper/CWT3VX7M

@misc{pith2026260622065,
  author       = {Pith},
  title        = {Pith review of: Boundary-Controlled Liouvillian Relaxation with Exact Steady States Fixed by Dissipative Disorder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CWT3VX7M}},
  note         = {Machine review of arXiv:2606.22065}
}
read the original abstract

In open quantum lattice systems, changing the boundary condition would appear to alter both the steady state and the nonzero Liouvillian spectrum. Here we show that boundary conditions can be used to control relaxation without changing the reduced steady state. In a disordered dissipative quantum link chain, the steady state is determined by an accumulated field defined by link-resolved dissipative disorder, and a gauge-generated transformation built from this field gives exact symmetry-resolved steady states with nonuniform, accumulated-field-dependent reduced matter occupations. We then construct a reciprocal cyclic boundary condition that preserves these matter occupations while changing the nonzero Liouvillian spectrum. Consequently, open and cyclic chains relax to the same reduced matter steady-occupation profile with different Liouvillian gaps with the cyclic closure accelerating relaxation. In the strong-dissipation limit, this relaxation difference can be reduced to a spectral comparison of effective exclusion processes with open and cyclic boundaries.

Figures

Figures reproduced from arXiv: 2606.22065 by the authors.

Figure 1
Figure 1. FIG. 1. Dissipative [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (c) shows that different accumulated-field Xn pro￾duce different OBC matter steady-occupation profiles, each ordered according to Eq. (11). Thus the many-body [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Liouvillian spectra in the zero weak-gauge block at [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Matter-occupation relaxation rates and Liouvillian [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Works this paper leans on

52 extracted references · 52 canonical work pages

  1. [1]

    E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Ex- ceptional topology of non-Hermitian systems, Rev. Mod. Phys.93, 015005 (2021)

    work page 2021

  2. [2]

    Okuma and M

    N. Okuma and M. Sato, Non-Hermitian Topological Phe- nomena: A Review, Annu. Rev. Condens. Matter Phys. 14, 83 (2023)

    work page 2023

  3. [3]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys.69, 249 (2020)

    work page 2020

  4. [4]

    Zhang, T

    X. Zhang, T. Zhang, M.-H. Lu, and Y.-F. Chen, A review on non-Hermitian skin effect, Adv. Phys.: X7, 2109431 (2022)

    work page 2022

  5. [5]

    Yao and Z

    S. Yao and Z. Wang, Edge states and topological invari- ants of non-Hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

    work page 2018

  6. [6]

    C. H. Lee and R. Thomale, Anatomy of skin modes and topology in non-Hermitian systems, Phys. Rev. B99, 201103(R) (2019)

    work page 2019

  7. [7]

    F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Biorthogonal bulk-boundary correspondence in non-Hermitian systems, Phys. Rev. Lett.121, 026808 (2018)

    work page 2018

  8. [8]

    F. Song, S. Yao, and Z. Wang, Non-Hermitian skin effect and chiral damping in open quantum systems, Phys. Rev. Lett.123, 170401 (2019)

    work page 2019

Show all 52 references
  1. [9]

    Ghatak, M

    A. Ghatak, M. Brandenbourger, J. van Wezel, and C. Coulais, Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial, Proc. Natl. Acad. Sci. U.S.A.117, 29561 (2020)

    2020

  2. [10]

    Weidemann, M

    S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, R. Thomale, and A. Szameit, Topological fun- neling of light, Science368, 311 (2020)

    2020

  3. [11]

    L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Non-Hermitian bulk-boundary correspondence in quantum dynamics, Nat. Phys.16, 761 (2020)

    2020

  4. [12]

    Helbig, T

    T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys.16, 747 (2020)

    2020

  5. [13]

    T. Haga, M. Nakagawa, R. Hamazaki, and M. Ueda, Liouvillian skin effect: Slowing down of relaxation pro- cesses without gap closing, Phys. Rev. Lett.127, 070402 (2021)

    2021

  6. [14]

    L. Mao, X. P. Yang, M.-J. Tao, H. P. Hu, and L. Pan, Liouvillian skin effect in a one-dimensional open many- body quantum system with generalized boundary condi- tions, Phys. Rev. B110, 045440 (2024)

    2024

  7. [15]

    Feng and S

    X. Feng and S. Chen, Boundary-sensitive Lindbladians and relaxation dynamics, Phys. Rev. B109, 014313 (2024)

    2024

  8. [16]

    Longhi, Erratic Non-Hermitian Skin Localization, Phys

    S. Longhi, Erratic Non-Hermitian Skin Localization, Phys. Rev. Lett.134, 196302 (2025)

    2025

  9. [17]

    Longhi, Erratic Liouvillian skin localization and sub- diffusive transport, Quantum Sci

    S. Longhi, Erratic Liouvillian skin localization and sub- diffusive transport, Quantum Sci. Technol.11, 025042 (2026)

    2026

  10. [18]

    Y. Z. Miao, W. Ding, L. T. Wang, X. L. Zhao, S. G. Liu, and X. X. Yi, Imaginary Gauge-steerable Edge Mode In Non-Hermitian Aubry-Andr´ e-Harper Model, Phys. Rev. A113, 0535093 (2026)

    2026

  11. [19]

    W. N. Faugno and T. Ozawa, Interaction-induced non- Hermitian topological phases from a dynamical gauge field, Phys. Rev. Lett.129, 180401 (2022)

    2022

  12. [20]

    H. Li, H. Wu, W. Zheng, and W. Yi, Many-body non- Hermitian skin effect under dynamic gauge coupling, Phys. Rev. Res.5, 033173 (2023)

    2023

  13. [21]

    M. C. Zheng, Y. Qiao, Y. P. Wang, J. P. Cao, and S. Chen, Exact Solution of the Bose-Hubbard Model with Unidirectional Hopping, Phys. Rev. Lett.132, 086502 (2024)

    2024

  14. [22]

    H.-R. Wang, B. Li, F. Song, and Z. Wang, Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain, SciPost Phys.15, 191 (2023)

    2023

  15. [23]

    J. B. Kogut, An introduction to lattice gauge theory and spin systems, Rev. Mod. Phys.51, 659 (1979)

    1979

  16. [24]

    J. B. Kogut, The lattice gauge theory approach to quan- tum chromodynamics, Rev. Mod. Phys.55, 775 (1983)

    1983

  17. [25]

    Fradkin,Field Theories of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2013)

    E. Fradkin,Field Theories of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2013)

    2013

  18. [26]

    Banerjee, M

    D. Banerjee, M. Dalmonte, M. M¨ uller, E. Rico, P. Ste- bler, U.-J. Wiese, and P. Zoller, Atomic Quantum Simu- lation of Dynamical Gauge Fields Coupled to Fermionic Matter: From String Breaking to Evolution after a Quench, Phys. Rev. Lett.109, 175302 (2012)

    2012

  19. [27]

    Zohar, J

    E. Zohar, J. I. Cirac, and B. Reznik, Quantum simula- tions of lattice gauge theories using ultracold atoms in optical lattices, Rep. Prog. Phys.79, 014401 (2015)

    2015

  20. [28]

    A. Mil, T. V. Zache, A. Hegde, A. Xia, R. P. Bhatt, M. K. Oberthaler, P. Hauke, J. Berges, and F. Jendrzejewski, A scalable realization of local U(1) gauge invariance in cold atomic mixtures, Science367, 1128 (2020)

    2020

  21. [29]

    B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Ob- servation of gauge invariance in a 71-site Bose-Hubbard quantum simulator, Nature587, 392 (2020)

    2020

  22. [30]

    Zhou, G.-X

    Z.-Y. Zhou, G.-X. Su, J. C. Halimeh, R. Ott, H. Sun, P. Hauke, B. Yang, Z.-S. Yuan, J. Berges, and J.-W. Pan, Thermalization dynamics of a gauge theory on a quantum simulator, Science377, 311 (2022). 7

    2022

  23. [31]

    Hauke, D

    P. Hauke, D. Marcos, M. Dalmonte, and P. Zoller, Quan- tum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions, Phys. Rev. X3, 041018 (2013)

    2013

  24. [32]

    E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zolleret al., Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Nature534, 516 (2016)

    2016

  25. [33]

    Y. T. Cheng and H. Zhai, EmergentU(1) lattice gauge theory in Rydberg atom arrays, Nat. Rev. Phys.6, 566 (2024)

    2024

  26. [34]

    Marcos, P

    D. Marcos, P. Rabl, E. Rico, and P. Zoller, Supercon- ducting Circuits for Quantum Simulation of Dynamical Gauge Fields, Phys. Rev. Lett.111, 110504 (2013)

    2013

  27. [35]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys.93, 025005 (2021)

    2021

  28. [36]

    Stannigel, P

    K. Stannigel, P. Hauke, D. Marcos, M. Hafezi, S. Diehl, M. Dalmonte, and P. Zoller, Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms, Phys. Rev. Lett.112, 120406 (2014)

    2014

  29. [37]

    J. C. Halimeh and P. Hauke, Reliability of Lattice Gauge Theories, Phys. Rev. Lett.125, 030503 (2020)

    2020

  30. [38]

    J. C. Halimeh, R. Ott, I. P. McCulloch, B. Yang, and P. Hauke, Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories, Phys. Rev. Res. 2, 033361 (2020)

    2020

  31. [39]

    J. C. Halimeh, H. F. Lang, J. Mildenberger, Z. Jiang, and P. Hauke, Gauge-symmetry protection using single-body terms, PRX Quantum2, 040311 (2021)

    2021

  32. [40]

    Syassen, D

    N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. Garc´ ıa-Ripoll, J. I. Cirac, G. Rempe, and S. D¨ urr, Strong Dissipation Inhibits Losses and Induces Correla- tions in Cold Molecular Gases, Science320, 1329 (2008)

    2008

  33. [41]

    Tomita, S

    T. Tomita, S. Nakajima, Y. Takasu, and Y. Takahashi, Dissipative Bose-Hubbard system with intrinsic two- body loss, Phys. Rev. A99, 031601(R) (2019)

    2019

  34. [42]

    Z. J. Wang, X.-D. Dai, H.-R. Wang, and Z. Wang, Topo- logically ordered steady states in open quantum systems, SciPost Phys.17, 167 (2024)

    2024

  35. [43]

    X.-D. Dai, Z. J. Wang, H.-R. Wang, and Z. Wang, Steady-state topological order, Phys. Rev. B111, 115142 (2025)

    2025

  36. [44]

    Y.-M. Hu, Z. J. Wang, B. Lian, and Z. Wang, Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model, Phys. Rev. Lett. 135, 260401 (2025)

    2025

  37. [45]

    Chandrasekharan and U.-J

    S. Chandrasekharan and U.-J. Wiese, Quantum link models: A discrete approach to gauge theories, Nucl. Phys. B492, 455 (1997)

    1997

  38. [46]

    Y. P. Huang, D. Banerjee, and M. Heyl, Dynamical Quantum Phase Transitions inU(1) Quantum Link Mod- els, Phys. Rev. Lett.122, 250401 (2019)

    2019

  39. [47]

    See Supplemental Material for the derivation of the Li- ouvillian branch construction, the strong-dissipation ef- fective exclusion process, and the OBC-to-CBC spectral comparison

  40. [48]

    E. M. Kessler, Generalized Schrieffer-Wolff formalism for dissipative systems, Phys. Rev. A86, 012126 (2012)

    2012

  41. [49]

    G. M. Sch¨ utz, Exact solution of the master equation for the asymmetric exclusion process, J. Stat. Phys.88, 427 (1997)

    1997

  42. [50]

    Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Phys

    B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Phys. Rep. 301, 65 (1998)

    1998

  43. [51]

    J. J. P. Veerman and R. Lyons, A Primer on Laplacian Dynamics in Directed Graphs, Nonlinear Phenom. Com- plex Syst.23, 196 (2020)

    2020

  44. [52]

    Y. Z. Miao and X. L. Zhao, Boundary-Controlled Li- ouvillian Relaxation with Exact Steady States Fixed by Dissipative Disorder data, [dataset], Zenodo (2026), 10.5281/zenodo.20779924

    2026 doi

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