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arxiv: 2510.15518 · v6 · submitted 2025-10-17 · ✦ hep-th · quant-ph

Photonic Exceptional Points in Holography and QCD

Mahdis Ghodrati This is my paper

Pith reviewed 2026-05-18 06:28 UTC · model grok-4.3

classification ✦ hep-th quant-ph
keywords photonic exceptional pointsholographic toy modelQCD theta-vacuumnon-Hermitian systemsmicrorings with gain and losstopological winding numbersLindblad formalism
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The pith

A holographic analogy constructs models of third-order photonic exceptional points and links them to second-order points in QCD theta vacua.

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

The paper uses an analogy with holographic confining geometries and complexified fields to create a toy model for third-order exceptional points in ternary coupled microrings that have gain and loss. It explores the spectral properties, sum rules, and behaviors like phase rigidity in these non-Hermitian systems, matching some experimental findings. It then extends the connection to the theta-vacuum in QCD by identifying shared topological features such as winding numbers and partition functions, locating a second-order exceptional point in a perturbed version of that model.

Core claim

Using an analogy with holographic confining geometries and complexified fields, the authors build a holographic toy model of third-order photonic exceptional points in ternary coupled microrings with gain and loss. They connect these to the theta-vacuum of QCD through topological structures, partition functions, and winding numbers, finding a second-order exceptional point in a perturbed theta-vacuum model.

What carries the argument

The analogy between holographic confining geometries and non-Hermitian gain-loss dynamics in microrings, enabling the mapping of exceptional point spectra and topological properties to QCD vacuum models.

If this is right

  • The Ferrell-Glover-Tinkham sum rule holds for various gain and loss combinations in the model.
  • Spectra behavior in the holographic lattice matches experimental results for three-site photonic EPs.
  • Phase rigidity and the Petermann factor show distinct behaviors around the exceptional points as parameters vary.
  • Complexified time-dependent entanglement entropy connects to exceptional points in non-Hermitian systems.
  • A controlled non-Hermitian deformation of the theta-vacuum toy model can be examined using the Lindblad formalism and Liouvillian eigenvalues.

Where Pith is reading between the lines

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

  • This approach suggests that photonic systems could be used to experimentally probe features of QCD theta vacua through the shared exceptional point structures.
  • Extensions to inhomogeneous holographic lattices might allow for the design of more complex exceptional point configurations.
  • The topological connections could imply new ways to understand non-Hermitian effects in high-energy physics models.
  • Further study of the Lindblad evolution might reveal dynamical aspects of the exceptional points in the QCD context.

Load-bearing premise

The structural analogy between holographic confining geometries and the non-Hermitian dynamics of gain-loss microrings faithfully captures the spectral and topological features of photonic exceptional points and the QCD theta vacuum.

What would settle it

Numerical computations of the model spectra that fail to reproduce the observed behaviors in experiments on ternary coupled microrings, or the absence of a second-order exceptional point when perturbing the theta-vacuum model as described.

Figures

Figures reproduced from arXiv: 2510.15518 by Mahdis Ghodrati.

Figure 1
Figure 1. Figure 1: The relationship between the real and imaginary parts of the eigenvalues versus frequency [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A ternary system, consisting of three coupled microrings. On the left, a PT-symmetric and on [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Modeling EPs using flavor branes in the bulk, showing the couplings and where the exceptional [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Two runs for finding eigenvalue trajectories in the complex plane as [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Two runs for finding imaginary parts versus [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Two runs for finding radial profiles of the dominant lasing eigenmode at the [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Phase diagram distinguishing the unbroken PT phase, where all eigenvalues are real, from the [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Ferrell-Glover-Tinkham sum rule for coupled ternary microcavities. This is a numerical demon [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: A 1d parameter sweep in the gain/loss (pumping) parameter γ, with coupling fixed. Here κ12 = κ23 = 0.15, κ13 = 0.06 and γ : 0 → 0.6, Nz = 20. In figure 11, the behavior of spectra at an EP is shown. To get this result, we use the holographic model, where we find the eigenvalues and eigenvectors of the full holographic block operator H. One could see that the general and qualitative behavior match the exper… view at source ↗
Figure 10
Figure 10. Figure 10: A coarse 2D parameter sweep (31 × 31) in the left. This figure shows the transfer fraction of spectral weight into the coherent lasing peak as a function of the coupling κ and pumping γ [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Example spectra at an EP candidate. This is the plot of [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Eigenvalue trajectories with the progression of gain/loss parameter [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Petermann factor and phase rigidities as a function of the coupling [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Petermann factor and phase rigidities as a function of gain/loss [PITH_FULL_IMAGE:figures/full_fig_p030_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The eigenfrequency solutions of (5.11) for the case of π + = π − = 0 [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The eigenfrequency solutions of (5.11) for the case of π + = π − = 1 [PITH_FULL_IMAGE:figures/full_fig_p034_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The eigenfrequency solutions of (5.11) for the case of π + = π − = 100. First, one can note that increasing the coupling κ clearly distinguishes the frequencies, as can be seen by comparing the behaviors of ω0 and ω1. This is similar to the result of [59], where, for instance, in a two-ring system, the sensitivity enhancement follows the square root of the coupling factor. On the other hand, these results… view at source ↗
Figure 18
Figure 18. Figure 18: The eigenfrequency solutions of 5.15 for the case [PITH_FULL_IMAGE:figures/full_fig_p036_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: The behavior of eqg versus ωn and π0 when perturbing the gain cavity only. Here, we set ϵ = 0.01 and κ = 1 on the left and ϵ = 0.5 and κ = 500 on the right. One can see that increasing κ and ϵ makes this plot smoother. The increase in κ has a bigger effect. Then, in the case of neutral cavity perturbation, where ϵ2 = ϵ and ϵ1 = ϵ3 = 0, equation 5.19 becomes eqn : ω 3 n − [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
Figure 20
Figure 20. Figure 20: The behavior of eqn versus ωn and π0 in the case of perturbing the neutral cavity only. Here, we set ϵ = 0.01 and κ = 1 on the left and ϵ = 0.5 and κ = 500 on the right. One can see that increasing κ and ϵ makes this plot smoother. The increase of κ has a bigger effect here as well. Comparing figures 19 and 21, one can see that for small ϵ and κ, the behavior is very similar, but increasing these two para… view at source ↗
Figure 21
Figure 21. Figure 21: The behavior of eqg,n versus ωn and π0, in perturbing the neutral cavity only, is shown for ϵ = 0.01, α = 0.1, and κ = 1 on the left; ϵ = 0.5, α = 0.1, and κ = 500 in the middle; and ϵ = 0.5, α = 0.9, and κ = 500 on the right. One can see that increasing κ and ϵ makes the plot smoother, with κ having the larger effect. One can see that increasing α makes the behavior of the system closer to the case of pe… view at source ↗
Figure 22
Figure 22. Figure 22: The behavior of the KD distribution versus the gain/loss parameter [PITH_FULL_IMAGE:figures/full_fig_p044_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The Schwinger-Keldysh (SK) representation of [PITH_FULL_IMAGE:figures/full_fig_p045_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: The real and imaginary parts of the timelike entanglement entropy, compared in magnitude [PITH_FULL_IMAGE:figures/full_fig_p047_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Schematic of the timelike tube E(U). Introducing EPs and non-Hermiticity into the system could shrink or distort E(U), cause multiple “branches” of solutions to emerge, or make the envelope boundaries ill-defined beyond null geodesics. 48 [PITH_FULL_IMAGE:figures/full_fig_p049_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: For various quark mass ratios γ ≡ m/ms = m2 π 2m2 K−m2 π , the behavior of the critical isospin chemical potential as a function of θ in QCD is shown. As in [88], the θ-vacuum of Quantum Chromodynamics, in terms of the winding number, can be defined as L θ QCD = −θw(x), (7.1) where here w(x) = g 2 16π 2 Tr[GµνG˜µν] (7.2) is the winding number density, and its integral R d 4x w(x) = ν is the winding number… view at source ↗
Figure 27
Figure 27. Figure 27: The result of a numerical simulation of the Schr¨odinger eigenproblem that searches the complex [PITH_FULL_IMAGE:figures/full_fig_p057_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Monodromy plots for various r. From top-left to bottom-right, r = 0.01, r = 0.03, r = 3, r = 10, and r = 20. The results came from a numerical simulation of the Schr¨odinger eigenproblem of [91], with small coupling ϵV (r) cos φ and searching for exceptional points. 8 Conclusion In this note, based on the behavior of fidelity susceptibility, chiral symmetry breaking, and the number of spectra and coalesci… view at source ↗
read the original abstract

In this work, based on an analogy with holographic confining geometries and using complexified fields, we build a holographic toy model of third order photonic exceptional points (EPs) of ternary coupled microrings with gain and loss, which makes an open, non-Hermitian quantum system. In our model, we discuss the Ferrell-Glover-Tinkham sum rule for various combinations of gain and loss systems, and numerically find the behavior of spectra which matches with the experiments. We also discuss the inhomogeneous case of a holographic lattice for three-site photonic EPs. Additionally, we numerically find the behavior of phase rigidity and the Petermann factor around EPs versus various parameters of the model. We also discuss the connections between recent developments in complexified, time-dependent entanglement entropy and EPs, and then, we connect EPs and the $\theta$-vacuum of QCD through topological structures, partition functions, and winding numbers, and find a second-order EP in a perturbed $\theta$-vacuum model. Finally, we examined a controlled non-Hermitian deformation of $\theta$-vacuum toy model, by using the Lindblad formalism and Liouvillian eigenvalues.

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 paper constructs a holographic toy model for third-order photonic exceptional points in ternary coupled microrings with gain and loss, drawing an analogy to holographic confining geometries and complexified fields. It numerically examines spectra (claiming matches to experiments), the Ferrell-Glover-Tinkham sum rule, phase rigidity, Petermann factors, inhomogeneous lattices, and connections to time-dependent entanglement entropy. The framework is then extended via topological structures, partition functions, and winding numbers to identify a second-order exceptional point in a perturbed θ-vacuum model of QCD, with further analysis using Lindblad formalism and Liouvillian eigenvalues.

Significance. If the analogy yields an emergent non-Hermitian boundary operator whose spectrum and Jordan structure arise from the bulk rather than by construction, the work could provide a useful bridge between holographic methods and non-Hermitian photonics, while offering a novel topological perspective on the QCD θ-vacuum. The reported numerical agreement with experimental spectra and the explicit treatment of phase rigidity/Petermann factors around EPs are concrete strengths; the link to complexified entanglement entropy is also potentially interesting. However, the absence of a derived dictionary weakens the claim that the exceptional-point features are holographically induced.

major comments (2)
  1. [Model construction and abstract] The central construction of the holographic toy model (described in the abstract and model section) introduces the gain-loss terms in the ternary microring Hamiltonian via structural analogy with complexified bulk fields and confining geometries, without an explicit holographic dictionary that derives the imaginary parts or Lindblad operators from the bulk action. This is load-bearing for the claim that the third-order EP (eigenvalue coalescence and eigenvector merging) emerges from the duality rather than being imposed by the choice of non-Hermitian parameters.
  2. [θ-vacuum and Lindblad analysis] In the extension to the perturbed θ-vacuum (final sections), the identification of a second-order EP via Liouvillian eigenvalues and winding numbers relies on the same analogy; it is unclear whether the coalescence is a consequence of the holographic setup or follows directly from the controlled non-Hermitian deformation chosen for the toy model. An explicit check that the Jordan-block structure survives under variations of the bulk complexification parameters would be required to support the topological connection.
minor comments (2)
  1. [Abstract and numerical results] The abstract states that spectra 'match with the experiments' but does not specify which experimental datasets, error bars, or quantitative measures of agreement are used; adding these details would improve reproducibility.
  2. [Model section] Notation for the gain/loss parameters and the precise form of the effective non-Hermitian operator should be introduced with an explicit equation early in the model section to avoid ambiguity when comparing to the bulk complexified fields.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions made to improve clarity regarding the toy-model nature of the work.

read point-by-point responses

  1. Referee: [Model construction and abstract] The central construction of the holographic toy model (described in the abstract and model section) introduces the gain-loss terms in the ternary microring Hamiltonian via structural analogy with complexified bulk fields and confining geometries, without an explicit holographic dictionary that derives the imaginary parts or Lindblad operators from the bulk action. This is load-bearing for the claim that the third-order EP (eigenvalue coalescence and eigenvector merging) emerges from the duality rather than being imposed by the choice of non-Hermitian parameters.

    Authors: We thank the referee for this observation. The manuscript explicitly describes the construction as a 'holographic toy model' built 'based on an analogy with holographic confining geometries and using complexified fields'. No complete holographic dictionary is claimed or derived; the gain-loss terms are introduced by structural analogy to explore non-Hermitian features in an effective boundary description. The numerical spectra, phase rigidity, and Petermann factors are computed directly within this effective model and compared to experiment. In the revised version we have added explicit language in the abstract and model section stating that the third-order EP is studied within the analogy-based framework rather than asserted to emerge strictly from a bulk-boundary duality. This clarification addresses the concern without changing the reported results. revision: yes

  2. Referee: [θ-vacuum and Lindblad analysis] In the extension to the perturbed θ-vacuum (final sections), the identification of a second-order EP via Liouvillian eigenvalues and winding numbers relies on the same analogy; it is unclear whether the coalescence is a consequence of the holographic setup or follows directly from the controlled non-Hermitian deformation chosen for the toy model. An explicit check that the Jordan-block structure survives under variations of the bulk complexification parameters would be required to support the topological connection.

    Authors: We agree that the θ-vacuum analysis employs the same analogy. The second-order EP is located via the topological invariants and Liouvillian spectrum of the controlled non-Hermitian deformation chosen to probe the connection. While an exhaustive parameter scan lies outside the present toy-model scope, we have added a short numerical check in the revised manuscript confirming that the Jordan-block structure persists under moderate variations of the deformation strength. This addition is noted in the final section and supports the robustness of the reported topological link within the explored regime. revision: partial

standing simulated objections not resolved
  • Deriving an explicit holographic dictionary that obtains the imaginary parts and Lindblad operators directly from a bulk action, which would require a substantially more complete holographic model than the analogy-based toy model presented here.

Circularity Check

0 steps flagged

No significant circularity; model built from analogy with independent numerical checks.

full rationale

The paper constructs a holographic toy model via explicit analogy to confining geometries and complexified fields, then performs numerical spectral analysis, phase rigidity calculations, and connections to QCD theta-vacuum via topological invariants. These steps do not reduce by the paper's own equations to a quantity defined solely by the input analogy or to a self-citation chain; the numerical behaviors and Lindblad/Liouvillian extensions are presented as computed outputs rather than tautological re-statements of the initial mapping. The analogy functions as a modeling ansatz rather than a self-definitional loop, and no load-bearing uniqueness theorem or fitted prediction is shown to collapse the central claims.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claims rest on the validity of the holographic analogy for non-Hermitian microring systems, the applicability of topological winding numbers to both EPs and the QCD vacuum, and the assumption that numerical spectra obtained with complexified fields faithfully represent physical gain-loss dynamics.

free parameters (1)
  • gain and loss parameters
    Varied across combinations to reproduce experimental spectra and to locate exceptional points
axioms (2)
  • domain assumption Holographic confining geometries provide a faithful analogy for the spectral properties of ternary coupled microrings with gain and loss
    Invoked to justify construction of the toy model
  • domain assumption Topological structures, partition functions, and winding numbers can be directly compared between photonic EPs and the QCD theta vacuum
    Basis for locating the second-order EP in the perturbed theta-vacuum model
invented entities (1)
  • holographic toy model of third-order photonic EPs no independent evidence
    purpose: To describe non-Hermitian dynamics of gain-loss microrings via complexified fields
    Constructed from the holographic analogy; no independent experimental confirmation supplied in abstract

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Reference graph

Works this paper leans on

93 extracted references · 93 canonical work pages · 11 internal anchors

  1. [1]

    Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity

    M. Ghodrati,Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity,Phys. Rev. D90(2014), no. 4 044055, [arXiv:1404.5399]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  2. [2]

    Ghodrati,Beyond AdS Space-times, New Holographic Correspondences and Applications, other thesis, 9, 2016

    M. Ghodrati,Beyond AdS Space-times, New Holographic Correspondences and Applications, other thesis, 9, 2016. 58

    work page 2016

  3. [3]

    On complexity growth in massive gravity theories, the effects of chirality and more

    M. Ghodrati,Complexity growth in massive gravity theories, the effects of chirality, and more,Phys. Rev. D96(2017), no. 10 106020, [arXiv:1708.07981]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  4. [4]

    Complexity growth rate during phase transitions

    M. Ghodrati,Complexity growth rate during phase transitions,Phys. Rev. D98(2018), no. 10 106011, [arXiv:1808.08164]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  5. [5]

    Ghodrati, X.-M

    M. Ghodrati, X.-M. Kuang, B. Wang, C.-Y. Zhang, and Y.-T. Zhou,The connection between holographic entanglement and complexity of purification,JHEP09(2019) 009, [arXiv:1902.02475]

    work page arXiv 2019

  6. [6]

    Y.-T. Zhou, M. Ghodrati, X.-M. Kuang, and J.-P. Wu,Evolutions of entanglement and complexity after a thermal quench in massive gravity theory,Phys. Rev. D100(2019), no. 6 066003, [arXiv:1907.08453]

    work page arXiv 2019

  7. [7]

    Ghodrati,Complexity and emergence of warped AdS 3 space-time from chiral Liouville action,JHEP02(2020) 052, [arXiv:1911.03819]

    M. Ghodrati,Complexity and emergence of warped AdS 3 space-time from chiral Liouville action,JHEP02(2020) 052, [arXiv:1911.03819]

    work page arXiv 2020

  8. [8]

    Ghodrati,Entanglement wedge reconstruction and correlation measures in mixed states: Modular flows versus quantum recovery channels,Phys

    M. Ghodrati,Entanglement wedge reconstruction and correlation measures in mixed states: Modular flows versus quantum recovery channels,Phys. Rev. D104(2021), no. 4 046004, [arXiv:2012.04386]

    work page arXiv 2021

  9. [9]

    Ghodrati,Correlations of mixed systems in confining backgrounds,Eur

    M. Ghodrati,Correlations of mixed systems in confining backgrounds,Eur. Phys. J. C82 (2022), no. 6 531, [arXiv:2110.12970]

    work page arXiv 2022

  10. [10]

    Ghodrati,Critical distance and Crofton form in confining geometries,J

    M. Ghodrati,Critical distance and Crofton form in confining geometries,J. Korean Phys. Soc.81(2022), no. 2 77–90, [arXiv:2205.03565]

    work page arXiv 2022

  11. [11]

    Ghodrati,Encoded information of mixed correlations: the views from one dimension higher,JHEP08(2023) 059, [arXiv:2209.04548]

    M. Ghodrati,Encoded information of mixed correlations: the views from one dimension higher,JHEP08(2023) 059, [arXiv:2209.04548]

    work page arXiv 2023

  12. [12]

    Ghodrati,String amplitudes and mutual information in confining backgrounds: the partonic behavior,arXiv:2307.13454

    M. Ghodrati,String amplitudes and mutual information in confining backgrounds: the partonic behavior,arXiv:2307.13454

    work page arXiv

  13. [13]

    Ghodrati and D

    M. Ghodrati and D. Gregoris,On the curvature invariants of the massive Banados–Teitelboim–Zanelli black holes and their holographic pictures,Int. J. Mod. Phys. A 37(2022), no. 34 2250202, [arXiv:2003.04412]

    work page arXiv 2022

  14. [14]

    Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity

    M. Ghodrati and A. Naseh,Phase transitions in Bergshoeff–Hohm–Townsend massive gravity,Class. Quant. Grav.34(2017), no. 7 075009, [arXiv:1601.04403]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  15. [15]

    Revisiting Conserved Charges in Higher Curvature Gravitational Theories

    M. Ghodrati, K. Hajian, and M. R. Setare,Revisiting Conserved Charges in Higher Curvature Gravitational Theories,Eur. Phys. J. C76(2016), no. 12 701, [arXiv:1606.04353]. 59

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  16. [16]

    Ghodrati,Chaos, phase transitions and curvature invariants of (rotating, warped, massive) BTZ black holes,AIP Conf

    M. Ghodrati,Chaos, phase transitions and curvature invariants of (rotating, warped, massive) BTZ black holes,AIP Conf. Proc.2874(2024), no. 1 020012, [arXiv:2202.05950]

    work page arXiv 2024

  17. [17]

    Schwinger Effect and Entanglement Entropy in Confining Geometries

    M. Ghodrati,Schwinger Effect and Entanglement Entropy in Confining Geometries,Phys. Rev. D92(2015), no. 6 065015, [arXiv:1506.08557]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  18. [18]

    A. T. Than et al.,The phase diagram of quantum chromodynamics in one dimension on a quantum computer,arXiv:2501.00579

    work page arXiv

  19. [19]

    Davoudi, C.-C

    Z. Davoudi, C.-C. Hsieh, and S. V. Kadam,Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer,Quantum8(Nov., 2024) 1520

    work page 2024

  20. [20]

    F. M. Surace, A. Lerose, O. Katz, E. R. Bennewitz, A. Schuckert, D. Luo, A. De, B. Ware, W. Morong, K. Collins, C. Monroe, Z. Davoudi, and A. V. Gorshkov,String-breaking dynamics in quantum adiabatic and diabatic processes, 2024

    work page 2024

  21. [21]

    A. De, A. Lerose, D. Luo, F. M. Surace, A. Schuckert, E. R. Bennewitz, B. Ware, W. Morong, K. S. Collins, Z. Davoudi, A. V. Gorshkov, O. Katz, and C. Monroe, Observation of string-breaking dynamics in a quantum simulator, 2024

    work page 2024

  22. [22]

    Belyansky, S

    R. Belyansky, S. Whitsitt, N. Mueller, A. Fahimniya, E. R. Bennewitz, Z. Davoudi, and A. V. Gorshkov,High-energy collision of quarks and mesons in the schwinger model: From tensor networks to circuit qed,Phys. Rev. Lett.132(Feb, 2024) 091903

    work page 2024

  23. [23]

    Saito,Photonic quantum chromodynamics,Frontiers in Physics11(Sept., 2023)

    S. Saito,Photonic quantum chromodynamics,Frontiers in Physics11(Sept., 2023)

    work page 2023

  24. [24]

    A. N. Ciavarella, C. W. Bauer, and J. C. Halimeh,Generic Hilbert Space Fragmentation in Kogut–Susskind Lattice Gauge Theories,arXiv:2502.03533

    work page arXiv

  25. [25]

    W. D. Heiss,The physics of exceptional points,Journal of Physics A: Mathematical and Theoretical45(Oct., 2012) 444016

    work page 2012

  26. [26]

    E. J. Bergholtz, J. C. Budich, and F. K. Kunst,Exceptional topology of non-Hermitian systems,Rev. Mod. Phys.93(2021), no. 1 015005, [arXiv:1912.10048]

    work page arXiv 2021

  27. [27]

    Fatemiabhari and C

    A. Fatemiabhari and C. Nunez,From conformal to confining field theories using holography, JHEP03(2024) 160, [arXiv:2401.04158]

    work page arXiv 2024

  28. [29]

    Bianchi, M

    M. Bianchi, M. Firrotta, J. Sonnenschein, and D. Weissman,Partonic behavior of string scattering amplitudes from holographic QCD models,JHEP05(2022) 058, [arXiv:2111.12106]. 60

    work page arXiv 2022

  29. [30]

    Z. Gong, M. Bello, D. Malz, and F. K. Kunst,Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths,Phys. Rev. Lett.129(2022), no. 22 223601, [arXiv:2205.05479]

    work page arXiv 2022

  30. [31]

    Z. Gong, M. Bello, D. Malz, and F. K. Kunst,Bound states and photon emission in non-Hermitian nanophotonics,Phys. Rev. A106(2022), no. 5 053517, [arXiv:2205.05490]

    work page arXiv 2022

  31. [32]

    Papadopoulos, P

    I. Papadopoulos, P. Wagner, G. Wunner, and J. Main,Bose-einstein condensates with attractive interaction: The case of self-trapping,Phys. Rev. A76(Nov, 2007) 053604

    work page 2007

  32. [33]

    Cartarius, J

    H. Cartarius, J. Main, and G. Wunner,Discovery of exceptional points in the bose-einstein condensation of gases with attractive interaction,Phys. Rev. A77(Jan, 2008) 013618

    work page 2008

  33. [34]

    Are´ an, K

    D. Are´ an, K. Landsteiner, and I. Salazar Landea,Non-hermitian holography,SciPost Phys. 9(2020), no. 3 032, [arXiv:1912.06647]

    work page arXiv 2020

  34. [35]

    Arean, D

    D. Arean, D. Garcia-Fari˜ na, and K. Landsteiner,Strongly Coupled PT-Symmetric Models in Holography, 11, 2024.arXiv:2411.18471

    work page arXiv 2024

  35. [36]

    Zhou and K

    X.-C. Zhou and K. Wang,Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities,arXiv:2405.01640

    work page arXiv

  36. [37]

    Z.-Y. Xian, D. Rodr´ ıguez Fern´ andez, Z. Chen, Y. Liu, and R. Meyer,Electric conductivity in non-Hermitian holography,SciPost Phys.16(2024), no. 1 004, [arXiv:2304.11183]

    work page arXiv 2024

  37. [38]

    W. Cai, S. Cao, X.-H. Ge, M. Matsumoto, and S.-J. Sin,Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models,Phys. Rev. D106(2022), no. 10 106010, [arXiv:2208.10800]

    work page arXiv 2022

  38. [39]

    St˚ alhammar, J

    M. St˚ alhammar, J. Larana-Aragon, L. Rødland, and F. K. Kunst,symmetry-protected exceptional cones and analogue Hawking radiation,New J. Phys.25(2023), no. 4 043012, [arXiv:2106.05030]

    work page arXiv 2023

  39. [40]

    Arean and D

    D. Arean and D. Garcia-Fari˜ na,Holographic Non-Hermitian Lattices and Junctions with PT-Restoring RG Flows,arXiv:2410.13584

    work page arXiv

  40. [41]

    Miri and A

    M.-A. Miri and A. Al´ u,Exceptional points in optics and photonics,Science363(2019)

    work page 2019

  41. [42]

    Jahangiri, G.-M

    M. Jahangiri, G.-M. Parsanasab, and L. Hajshahvaladi,Observation of anti-pt-symmetry and higher-order exceptional point pt-symmetry in ternary systems for single-mode operation,Scientific Reports15(2025), no. 1 4823

    work page 2025

  42. [43]

    D’Achille, M

    M. D’Achille, M. G¨ arttner, and T. Haas,Configurable photonic simulator for quantum field dynamics,arXiv:2506.23838. 61

    work page arXiv

  43. [44]

    Michel, W

    N. Michel, W. Nazarewicz, J. Oko lowicz, and M. P loszajczak,Open problems in the theory of nuclear open quantum systems,Journal of Physics G: Nuclear and Particle Physics37 (may, 2010) 064042

    work page 2010

  44. [45]

    W. D. Heiss,Chirality of wavefunctions for three coalescing levels,Journal of Physics A: Mathematical and Theoretical41(jun, 2008) 244010

    work page 2008

  45. [46]

    W. D. Heiss and S. Radu,Quantum chaos, degeneracies, and exceptional points,Phys. Rev. E52(Nov, 1995) 4762–4767

    work page 1995

  46. [47]

    M. V. Berry and M. Tabor,Level Clustering in the Regular Spectrum,Proceedings of the Royal Society of London Series A356(Sept., 1977) 375–394

    work page 1977

  47. [48]

    Bianchi, M

    M. Bianchi, M. Firrotta, J. Sonnenschein, and D. Weissman,Measure for Chaotic Scattering Amplitudes,Phys. Rev. Lett.129(2022), no. 26 261601, [arXiv:2207.13112]

    work page arXiv 2022

  48. [49]

    Bianchi, M

    M. Bianchi, M. Firrotta, J. Sonnenschein, and D. Weissman,Measuring chaos in string scattering processes,Phys. Rev. D108(2023), no. 6 066006, [arXiv:2303.17233]

    work page arXiv 2023

  49. [50]

    Savi´ c and M

    N. Savi´ c and M.ˇCubrovi´ c,Weak chaos and mixed dynamics in the string S-matrix,JHEP 03(2024) 101, [arXiv:2401.02211]

    work page arXiv 2024

  50. [51]

    W. D. Heiss and A. L. Sannino,Transitional regions of finite fermi systems and quantum chaos,Phys. Rev. A43(Apr, 1991) 4159–4166

    work page 1991

  51. [52]

    Golubitsky and W

    M. Golubitsky and W. Langford,Pattern formation and bistability in flow between counterrotating cylinders,Physica D: Nonlinear Phenomena32(1988), no. 3 362–392

    work page 1988

  52. [53]

    K. Qu, S. Meuren, and N. J. Fisch,Creating pair plasmas with observable collective effects, Plasma Physics and Controlled Fusion65(Feb., 2023) 034007

    work page 2023

  53. [54]

    Wiersig,Petermann factors and phase rigidities near exceptional points,Phys

    J. Wiersig,Petermann factors and phase rigidities near exceptional points,Phys. Rev. Res.5 (Jul, 2023) 033042

    work page 2023

  54. [55]

    W. D. Heiss,Repulsion of resonance states and exceptional points,Phys. Rev. E61(Jan,

    work page

  55. [56]

    M. H. Teimourpour, R. El-Ganainy, A. Eisfeld, A. Szameit, and D. N. Christodoulides,Light transport inPT-invariant photonic structures with hidden symmetries,Phys. Rev. A90 (Nov, 2014) 053817

    work page 2014

  56. [57]

    Wiersig,Petermann factors and phase rigidities near exceptional points,Phys

    J. Wiersig,Petermann factors and phase rigidities near exceptional points,Phys. Rev. Res.5 (2023), no. 3 033042, [arXiv:2304.00764]. 62

    work page arXiv 2023

  57. [58]

    Effective Lagrangian approach to vector mesons, their structure and decays$^{*)}$

    F. Klingl, N. Kaiser, and W. Weise,Effective Lagrangian approach to vector mesons, their structure and decays,Z. Phys. A356(1996), no. 2 193–206, [hep-ph/9607431]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  58. [59]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan,Enhanced sensitivity at higher-order exceptional points,Nature548(2017), no. 7666 187–191

    work page 2017

  59. [60]

    Liu, C.-Y

    X.-L. Liu, C.-Y. Yue, J. Nian, and W. Zheng,Quantum-Corrected Holographic Wilson Loop Correlators and Confinement,arXiv:2412.11107

    work page arXiv

  60. [61]

    Hodaei, M.-A

    H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Parity-time–symmetric microring lasers,Science346(2014), no. 6212 1258480

    work page 2014

  61. [62]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen,Can quantum-mechanical description of physical reality be considered complete?,Phys. Rev.47(May, 1935) 777–780

    work page 1935

  62. [63]

    Gisin and A

    N. Gisin and A. Go,Epr test with photons and kaons: Analogies,American Journal of Physics69(Mar., 2001) 264–270. [64]STARCollaboration,Probing QCD Confinement with Spin Entanglement, arXiv:2506.05499

    work page arXiv 2001

  63. [64]

    X. Cao, M. Baggioli, H. Liu, and D. Li,Pion dynamics in a soft-wall ads-qcd model,Journal of High Energy Physics2022(Dec., 2022)

    work page 2022

  64. [65]

    Debnath, Y

    K. Debnath, Y. Zhang, and K. Mølmer,Lasing in the superradiant crossover regime,Phys. Rev. A98(Dec, 2018) 063837

    work page 2018

  65. [66]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi, and Y. Taki,Timelike entanglement entropy,JHEP05(2023) 052, [arXiv:2302.11695]

    work page arXiv 2023

  66. [67]

    Milekhin, Z

    A. Milekhin, Z. Adamska, and J. Preskill,Observable and computable entanglement in time, arXiv:2502.12240

    work page arXiv

  67. [68]

    Xu and W.-z

    J. Xu and W.-z. Guo,Imaginary part of timelike entanglement entropy,JHEP02(2025) 094, [arXiv:2410.22684]

    work page arXiv 2025

  68. [69]

    Glorioso, X.-L

    P. Glorioso, X.-L. Qi, and Z. Yang,Space-time generalization of mutual information,JHEP 05(2024) 338, [arXiv:2401.02475]

    work page arXiv 2024

  69. [70]

    Nunez and D

    C. Nunez and D. Roychowdhury,Time-like Entanglement Entropy: a top-down approach, arXiv:2505.20388

    work page arXiv

  70. [71]

    Guo and J

    W.-z. Guo and J. Xu,A duality of Ryu-Takayanagi surfaces inside and outside the horizon, arXiv:2502.16774. 63

    work page arXiv

  71. [72]

    Ikeda,Timelike Quantum Energy Teleportation,arXiv:2504.05353

    K. Ikeda,Timelike Quantum Energy Teleportation,arXiv:2504.05353

    work page arXiv

  72. [73]

    Narayan and H

    K. Narayan and H. K. Saini,Notes on time entanglement and pseudo-entropy,Eur. Phys. J. C84(2024), no. 5 499, [arXiv:2303.01307]

    work page arXiv 2024

  73. [74]

    Nunez and D

    C. Nunez and D. Roychowdhury,Interpolating between Space-like and Time-like Entanglement via Holography,arXiv:2507.17805

    work page arXiv

  74. [75]

    Hales, U

    J. Hales, U. Bajpai, T. Liu, D. R. Baykusheva, M. Li, M. Mitrano, and Y. Wang,Witnessing light-driven entanglement using time-resolved resonant inelastic x-ray scattering,Nature Communications14(2023), no. 1 3512

    work page 2023

  75. [76]

    F. U. J. Klauck, M. Heinrich, A. Szameit, and T. A. W. Wolterink,Crossing exceptional points in non-hermitian quantum systems,Science Advances11(Jan., 2025)

    work page 2025

  76. [77]

    M. B. Hastings and T. Koma,Spectral gap and exponential decay of correlations,Commun. Math. Phys.265(2006) 781–804, [math-ph/0507008]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  77. [78]

    Nachtergaele, Y

    B. Nachtergaele, Y. Ogata, and R. Sims,Propagation of correlations in quantum lattice systems,Journal of Statistical Physics124(July, 2006) 1–13

    work page 2006

  78. [79]

    J. W. Yoon, Y. Choi, C. Hahn, G. Kim, S. H. Song, K.-Y. Yang, J. Y. Lee, Y. Kim, C. S. Lee, J. K. Shin, H.-S. Lee, and P. Berini,Time-asymmetric loop around an exceptional point over the full optical communications band,Nature562(2018), no. 7725 86–90

    work page 2018

  79. [80]

    H.-Z. Chen, T. Liu, H.-Y. Luan, R.-J. Liu, X.-Y. Wang, X.-F. Zhu, Y.-B. Li, Z.-M. Gu, S.-J. Liang, H. Gao, L. Lu, L. Ge, S. Zhang, J. Zhu, and R.-M. Ma,Revealing the missing dimension at an exceptional point,Nature Physics16(2020), no. 5 571–578

    work page 2020

  80. [81]

    X. Dong, A. Lewkowycz, and M. Rangamani,Deriving covariant holographic entanglement, JHEP11(2016) 028, [arXiv:1607.07506]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

Showing first 80 references.