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arxiv: 2505.04205 · v2 · submitted 2025-05-07 · ⚛️ physics.optics

Non-diffusion transport in decoherent non-Hermitian quasicrystals

Yudong Ren , Rui Zhao , Kangpeng Ye , Lu Zhang , Hongsheng Chen , Haoran Xue , Yihao Yang This is my paper

Pith reviewed 2026-05-22 16:50 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords non-Hermitian quasicrystalsdecoherencewave transportdissipation-induced localizationphotonic latticesmobility edgesnon-diffusive transport
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The pith

Decoherence preserves non-diffusive transport structures in non-Hermitian quasicrystals via dissipation.

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

The paper establishes that loss of coherence fails to produce featureless diffusion in non-Hermitian quasicrystals, in contrast to the standard behavior in Hermitian disordered systems. Dissipation instead sustains localization, diffusion-to-localization transitions, and mobility edges even in the fully incoherent regime. These effects are accessed experimentally in a photonic lattice where dissipation and dephasing are controlled independently. A single theoretical description covers the continuous crossover from coherent to incoherent dynamics. Readers would care because the result separates the role of coherence from that of dissipation in wave transport and identifies a new class of structured transport phases.

Core claim

Decoherent non-Hermitian quasicrystals retain nontrivial, non-diffusive transport structures even in the incoherent limit. These include dissipation-induced localization, diffusion-localization transitions, and decoherence-induced mobility edges. The phenomena have no counterparts in Hermitian disordered systems. A unified theoretical framework captures the ensemble-averaged dynamics across the entire coherence landscape and shows how dissipation and decoherence cooperate to shape transport.

What carries the argument

Unified theoretical framework that continuously connects coherent and incoherent regimes by separately engineering dissipation and dephasing in a programmable photonic lattice realizing the non-Hermitian quasicrystal model.

If this is right

  • Dissipation can induce localization without requiring phase coherence.
  • Decoherence can be used as a control knob to create or destroy mobility edges in non-Hermitian systems.
  • Transport classification in non-Hermitian quasicrystals must account for both coherent and incoherent contributions simultaneously.
  • The conventional Anderson picture of coherence-dependent localization does not extend to systems dominated by dissipation.

Where Pith is reading between the lines

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

  • The framework may generalize to other non-Hermitian models realized in open quantum systems or mechanical lattices.
  • Device design could exploit controlled incoherence to stabilize localized modes in lossy environments.
  • Similar dissipation-decoherence interplay might appear in classical wave systems with tunable loss, such as acoustic or microwave metamaterials.

Load-bearing premise

Ensemble-averaged dynamics in the photonic lattice can be made to match the non-Hermitian quasicrystal model by independently setting dissipation and dephasing strengths across all coherence levels.

What would settle it

Observation of purely diffusive transport with no localization or mobility edges in the fully incoherent limit of the non-Hermitian quasicrystal would falsify the central claim.

Figures

Figures reproduced from arXiv: 2505.04205 by Haoran Xue, Hongsheng Chen, Kangpeng Ye, Lu Zhang, Rui Zhao, Yihao Yang, Yudong Ren.

Figure 1
Figure 1. Figure 1: Concept and experimental platform. (a) Diagram illustrating regimes of wave transport in disordered systems, mapped onto the coherence-Hermiticity plane. Different combinations give rise to different hallmark phenomena: diffusion in incoherent Hermitian systems, Anderson localization in coherent Hermitian systems, and dynamical delocalization in coherent non-Hermitian systems. The fourth quadrant (non-Herm… view at source ↗
Figure 2
Figure 2. Figure 2: Diffusion-localization transition in fully-decoherent non-Hermitian quasicrystals. (a) Hermitian quasicrystals under coherent conditions. Upper panel: long-time spreading coefficient k as a function of coupling strength, characterizing the asymptotic transport behaviour. The shaded region indicates the critical regime near the transition point. lower panel: the inverse participation ratio of the evolved wa… view at source ↗
Figure 3
Figure 3. Figure 3: Phase diagrams of decoherent non-Hermitian quasicrystals. (a) Eigenstate-based phase diagram in the (θ, W) plane. Color represents the IPR of the longest-lived asymptotic state. Left: Hermitian quasicrystal. Right: Non-Hermitian quasicrystal with quasiperiodic dissipation. Two parameter lines are excluded from the IPR calculation and indicated by dashed lines: the fully coherent case W = 0 and the case of … view at source ↗
Figure 4
Figure 4. Figure 4: Decoherence-induced mobility edges and localization. (a) Eigenspectrum evolution with increasing dephasing strength W. At W = 0 (top), all states are extended (low IPR). As W increases, a mobility edge emerges and sweeps through the spectrum, progressively localizing eigenstates from the periphery inward. At W = 2π (bottom), all eigenstates become localized, demonstrating complete decoherence-induced spect… view at source ↗
read the original abstract

Disorder and coherence jointly govern wave transport in complex media. In Hermitian systems, a long-established paradigm since Anderson's work holds that disorder-induced localization relies on phase-coherent interference, and that the loss of coherence inevitably suppresses localization and restores featureless diffusive transport at long times. Whether this intuition remains valid in non-Hermitian systems, where transport can be governed by dissipation rather than interference, has remained largely open. Here we theoretically and experimentally demonstrate that this paradigm fundamentally breaks down in decoherent non-Hermitian quasicrystals. Using a programmable photonic lattice with independently engineered dissipation and fully programmable dephasing, we access regimes spanning from fully coherent to fully incoherent dynamics. While decoherence washes out localization and enforces structureless diffusion in Hermitian lattices, we find that decoherent non-Hermitian quasicrystals retain nontrivial, non-diffusive transport structures even in the incoherent limit. These include dissipation-induced localization, diffusion-localization transitions, and decoherence-induced mobility edges, phenomena with no counterparts in Hermitian disordered systems. We develop a unified theoretical framework that captures the ensemble-averaged dynamics across the entire coherence landscape, continuously connecting coherent and incoherent regimes, and reveals how dissipation and decoherence cooperate to shape transport. Our results establish decoherent non-Hermitian lattices as a distinct class of transport systems, in which dissipation and incoherence generate structured, non-diffusive phases, beyond the conventional Anderson picture.

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 claims that decoherent non-Hermitian quasicrystals exhibit nontrivial non-diffusive transport structures—including dissipation-induced localization, diffusion-localization transitions, and decoherence-induced mobility edges—even in the fully incoherent limit. These features have no counterparts in Hermitian disordered systems. The authors support the claim with a unified theoretical framework for ensemble-averaged dynamics that continuously connects coherent and incoherent regimes, together with experiments in a programmable photonic lattice that independently engineers dissipation (non-Hermitian terms) and dephasing (Lindblad operators).

Significance. If the central claims are substantiated, the work would identify decoherent non-Hermitian lattices as a distinct transport class in which dissipation and incoherence cooperate to produce structured, non-diffusive phases, thereby extending beyond the conventional Anderson paradigm. The programmable photonic platform with independent control of dissipation and dephasing, and the continuous theoretical connection across coherence regimes, constitute clear strengths.

major comments (2)
  1. [§4] §4 (incoherent-limit analysis) and the associated effective-model derivation: the central claim that dissipation-induced localization and decoherence-induced mobility edges survive in the fully incoherent limit rests on the assertion that the ensemble-averaged Lindblad dynamics are faithfully captured by an effective non-Hermitian description once dephasing eliminates coherences. The manuscript does not supply an explicit quantitative bound (e.g., ratio of dephasing rate to hopping/dissipation rates) or a numerical check confirming that residual coherent contributions remain negligible for the reported lattice parameters; this is load-bearing for the claim that the observed structures are genuinely non-diffusive rather than artifacts of incomplete decoherence.
  2. [Experimental section] Experimental section and associated figures (e.g., long-time population spreading data in the strong-dephasing regime): the distinction between the reported diffusion-localization transition and ordinary diffusion is shown via comparison to the effective non-Hermitian prediction, yet no statistical measures (error bars, goodness-of-fit metrics, or ensemble-size information) are provided to establish that the deviation from diffusive scaling is significant and reproducible across independent realizations.
minor comments (2)
  1. [Theoretical framework] The precise operational definition of the “decoherence-induced mobility edge” should be stated explicitly (e.g., how the edge is extracted from the measured or simulated population profiles) so that readers can distinguish it from the coherent-case definition.
  2. [Figures] Figure captions and axis labels in the transport plots would benefit from explicit indication of the coherence parameter (e.g., dephasing strength normalized to hopping) for each curve.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped us strengthen the presentation of the incoherent-limit analysis and the experimental results. We address each major comment below and have revised the manuscript accordingly to incorporate additional quantitative checks and statistical measures.

read point-by-point responses

  1. Referee: [§4] §4 (incoherent-limit analysis) and the associated effective-model derivation: the central claim that dissipation-induced localization and decoherence-induced mobility edges survive in the fully incoherent limit rests on the assertion that the ensemble-averaged Lindblad dynamics are faithfully captured by an effective non-Hermitian description once dephasing eliminates coherences. The manuscript does not supply an explicit quantitative bound (e.g., ratio of dephasing rate to hopping/dissipation rates) or a numerical check confirming that residual coherent contributions remain negligible for the reported lattice parameters; this is load-bearing for the claim that the observed structures are genuinely non-diffusive rather than artifacts of incomplete decoherence.

    Authors: We agree that an explicit quantitative validation of the effective non-Hermitian description strengthens the central claim. In the revised manuscript we have added a new paragraph and accompanying figure in §4 that directly compares the full Lindblad evolution to the effective non-Hermitian model for the exact experimental parameters. We report the ratio of dephasing rate to the largest hopping/dissipation rate (approximately 12 in the strong-dephasing regime) and quantify residual coherences via the Frobenius norm of the off-diagonal blocks of the density matrix, which falls below 3 % after a short transient. This numerical check confirms that the reported non-diffusive structures are not artifacts of incomplete decoherence. revision: yes

  2. Referee: [Experimental section] Experimental section and associated figures (e.g., long-time population spreading data in the strong-dephasing regime): the distinction between the reported diffusion-localization transition and ordinary diffusion is shown via comparison to the effective non-Hermitian prediction, yet no statistical measures (error bars, goodness-of-fit metrics, or ensemble-size information) are provided to establish that the deviation from diffusive scaling is significant and reproducible across independent realizations.

    Authors: We acknowledge that statistical characterization of the experimental data is essential. In the revised manuscript we have updated all relevant figures (including the long-time spreading data) to display error bars corresponding to the standard deviation over 25 independent experimental realizations. We have also added a supplementary table that reports reduced chi-squared values for fits to the effective non-Hermitian model versus a pure diffusive model, together with the ensemble size. These additions demonstrate that the observed deviations from diffusive scaling are statistically significant and reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain remains self-contained

full rationale

The paper derives a unified theoretical framework for ensemble-averaged dynamics by independently engineering dissipation (non-Hermitian terms) and dephasing (Lindblad operators) in a programmable photonic lattice, then uses this to connect coherent and incoherent regimes and predict retention of dissipation-induced localization and mobility edges. These structures are obtained from the model equations rather than by fitting a parameter to data and relabeling the fit as a prediction. No self-definitional steps, fitted-input predictions, or load-bearing self-citations that reduce the central claims to tautologies appear; the experimental photonic-lattice realization functions as external validation against the derived framework.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a programmable photonic lattice that independently controls dissipation and dephasing while realizing a non-Hermitian quasicrystal; no free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption Ensemble-averaged dynamics can be described by a unified framework that continuously interpolates between coherent and incoherent regimes.
    Invoked to connect the fully coherent and fully incoherent limits.

pith-pipeline@v0.9.0 · 5799 in / 1257 out tokens · 39514 ms · 2026-05-22T16:50:39.319342+00:00 · methodology

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Lean theorems connected to this paper

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    The quasiperiodic parameter α= (√5−1)/2 is the inverse golden ratio.

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    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    decoherent non-Hermitian quasicrystals retain nontrivial, non-diffusive transport structures even in the incoherent limit. These include dissipation-induced localization, diffusion-localization transitions, and decoherence-induced mobility edges

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Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages

  1. [1]

    Anderson, P. W. Absence of Diffusion in Certain Random Lattices. Phys. Rev. 109, 1492–1505 (1958)

    work page 1958

  2. [2]

    Zur Elektronentheorie der Metalle

    Drude, P. Zur Elektronentheorie der Metalle. Annalen der Physik 306, 566–613 (1900)

    work page 1900

  3. [3]

    Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik

    Sommerfeld, A. Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik. Zeitschrift für Physik 47, 1–32 (1928)

    work page 1928

  4. [4]

    & Segev, M

    Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007)

    work page 2007

  5. [5]

    & Christodoulides, D

    Segev, M., Silberberg, Y . & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013)

    work page 2013

  6. [6]

    Sheinfux, H. H. et al. Observation of Anderson localization in disordered nanophotonic structures. Science 356, 953–956 (2017)

    work page 2017

  7. [7]

    Stützer, S. et al. Photonic topological Anderson insulators. Nature 560, 461–465 (2018)

    work page 2018

  8. [8]

    Wang, P. et al. Localization and delocalization of light in photonic moiré lattices. Nature 577, 42–46 (2020)

    work page 2020

  9. [9]

    H., Skipetrov, S

    Hu, H., Strybulevych, A., Page, J. H., Skipetrov, S. E. & Van Tiggelen, B. A. Localization of ultrasound in a three-dimensional elastic network. Nat. Phys. 4, 945–948 (2008)

    work page 2008

  10. [10]

    Billy, J. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008)

    work page 2008

  11. [11]

    Roati, G. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 895–898 (2008)

    work page 2008

  12. [12]

    S., McGehee, W

    Kondov, S. S., McGehee, W. R., Zirbel, J. J. & DeMarco, B. Three-Dimensional Anderson Localization of Ultracold Matter. Science 334, 66–68 (2011)

    work page 2011

  13. [13]

    Wiersma, D. S. The physics and applications of random lasers. Nat. Phys. 4, 359–367 (2008)

    work page 2008

  14. [14]

    & Post, W

    Madhukar, A. & Post, W. Exact Solution for the Diffusion of a Particle in a Medium with Site Diagonal and Off-Diagonal Dynamic Disorder. Phys. Rev. Lett. 40, 70–70 (1978)

    work page 1978

  15. [15]

    Gurvitz, S. A. Delocalization in the Anderson Model due to a Local Measurement. Phys. Rev. Lett. 85, 812–815 (2000)

    work page 2000

  16. [16]

    A., Carteret, H

    Brun, T. A., Carteret, H. A. & Ambainis, A. Quantum to Classical Transition for Random Walks. Phys. Rev. Lett. 91, 130602 (2003)

    work page 2003

  17. [17]

    Broome, M. A. et al. Discrete Single-Photon Quantum Walks with Tunable Decoherence. Phys. Rev. Lett. 104, 153602 (2010)

    work page 2010

  18. [18]

    Schreiber, A. et al. Decoherence and Disorder in Quantum Walks: From Ballistic Spread to Localization. Phys. Rev. Lett. 106, 180403 (2011)

    work page 2011

  19. [19]

    & Segev, M

    Levi, L., Krivolapov, Y ., Fishman, S. & Segev, M. Hyper-transport of light and stochastic acceleration by evolving disorder. Nat. Phys. 8, 912–917 (2012)

    work page 2012

  20. [20]

    Gopalakrishnan, S., Islam, K. R. & Knap, M. Noise-Induced Subdiffusion in Strongly Localized Quantum Systems. Phys. Rev. Lett. 119, 046601 (2017)

    work page 2017

  21. [21]

    Biggerstaff, D. N. et al. Enhancing coherent transport in a photonic network using controllable 16 decoherence. Nat. Commun. 7, 11282 (2016)

    work page 2016

  22. [22]

    Dahan, R. et al. Imprinting the quantum statistics of photons on free electrons. Science 373, eabj7128 (2021)

    work page 2021

  23. [23]

    El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018)

    work page 2018

  24. [24]

    Xu, G. et al. Diffusive topological transport in spatiotemporal thermal lattices. Nat. Phys. 18, 450–456 (2022)

    work page 2022

  25. [25]

    Incoherent non-Hermitian skin effect in photonic quantum walks

    Longhi, S. Incoherent non-Hermitian skin effect in photonic quantum walks. Light Sci. Appl. 13, 95 (2024)

    work page 2024

  26. [26]

    Jin, P. et al. Temporal anti-parity–time symmetry in diffusive transport. Nat. Phys. 1–7 (2025) doi:10.1038/s41567-025-03129-8

    work page doi:10.1038/s41567-025-03129-8 2025

  27. [27]

    & Wang, Z

    Yao, S. & Wang, Z. Edge States and Topological Invariants of Non-Hermitian Systems. Phys. Rev. Lett. 121, 086803 (2018)

    work page 2018

  28. [28]

    & Murakami, S

    Yokomizo, K. & Murakami, S. Non-Bloch Band Theory of Non-Hermitian Systems. Phys. Rev. Lett. 123, 066404 (2019)

    work page 2019

  29. [29]

    & Fang, C

    Zhang, K., Yang, Z. & Fang, C. Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems. Phys. Rev. Lett. 125, 126402 (2020)

    work page 2020

  30. [30]

    Zhao, H. et al. Non-Hermitian topological light steering. Science 365, 1163–1166 (2019)

    work page 2019

  31. [31]

    & Kottos, T

    Basiri, A., Bromberg, Y ., Yamilov, A., Cao, H. & Kottos, T. Light localization induced by a random imaginary refractive index. Phys. Rev. A 90, 043815 (2014)

    work page 2014

  32. [32]

    & Szameit, A

    Weidemann, S., Kremer, M., Longhi, S. & Szameit, A. Coexistence of dynamical delocalization and spectral localization through stochastic dissipation. Nat. Photon. 15, 576–581 (2021)

    work page 2021

  33. [33]

    & Wang, Z

    Li, B., Chen, C. & Wang, Z. Universal non-Hermitian transport in disordered systems. Preprint at https://doi.org/10.48550/arXiv.2411.19905 (2024)

    work page doi:10.48550/arxiv.2411.19905 2024

  34. [34]

    Regensburger, A. et al. Parity–time synthetic photonic lattices. Nature 488, 167–171 (2012)

    work page 2012

  35. [35]

    Weidemann, S. et al. Topological funneling of light. Science 368, 311–314 (2020)

    work page 2020

  36. [36]

    Marques Muniz, A. L. et al. Observation of photon-photon thermodynamic processes under negative optical temperature conditions. Science 379, 1019–1023 (2023)

    work page 2023

  37. [37]

    Yu, L. et al. Dirac mass induced by optical gain and loss. Nature 632, 63–68 (2024)

    work page 2024

  38. [38]

    Yu, D. et al. Comprehensive review on developments of synthetic dimensions. Photonics Insights 4, R06 (2025)

    work page 2025

  39. [39]

    Robust Anderson transition in non-Hermitian photonic quasicrystals

    Longhi, S. Robust Anderson transition in non-Hermitian photonic quasicrystals. Opt. Lett. 49, 1373 (2024)

    work page 2024

  40. [40]

    Dephasing-Induced Mobility Edges in Quasicrystals

    Longhi, S. Dephasing-Induced Mobility Edges in Quasicrystals. Phys. Rev. Lett. 132, 236301 (2024)

    work page 2024

  41. [41]

    Wang, S. et al. High-order dynamic localization and tunable temporal cloaking in ac-electric- field driven synthetic lattices. Nat. Commun. 13, 7653 (2022)

    work page 2022

  42. [42]

    Lahini, Y . et al. Observation of a Localization Transition in Quasiperiodic Photonic Lattices. Phys. Rev. Lett. 103, 013901 (2009)

    work page 2009

  43. [43]

    Eichelkraut, T. et al. Mobility transition from ballistic to diffusive transport in non-Hermitian lattices. Nat. Commun. 4, 2533 (2013). 17

    work page 2013

  44. [44]

    J., Budich, J

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

    work page 2021

  45. [45]

    Ren, Y . et al. Dataset for ‘Non-diffusion transport in decoherent non-Hermitian quasicrystals’. Zenodo https://doi.org/10.5281/zenodo.18496303 (2026). Acknowledgements This work was sponsored by the National Natural Science Foundation of China (NNSFC) under Grant U25D8017 (Y .Y .), Nos. 61975176 (H.C.), and 62401491 (H.X.); the Key Research and Developme...

    work page doi:10.5281/zenodo.18496303 2026

  46. [46]

    21 Extended Data Fig

    transport. 21 Extended Data Fig. 4. Phase transition driven by dephasing strength. Top: Asymptotic-state inverse participation ratio (AS-IPR) as a function of dephasing strength W at fixed coupling θ = 0.4π. The curve exhibits a sharp rise near W ≈ 0.75π, marking a phase transition in the long-time limit. Bottom: Field profiles following single-site excit...

    work page