pith. sign in

arxiv: 2511.03600 · v2 · submitted 2025-11-05 · 🌊 nlin.PS · physics.optics· quant-ph

Stability of the Quantum Coherent Superradiant States in Relation to Exciton-Phonon Interactions and the Fundamental Soliton in Hybrid Perovskites

A. A. Gladkij , N. A. Veretenov , N. N. Rosanov , B. A. Malomed , V. Al. Osipov , B. D. Fainberg This is my paper

Pith reviewed 2026-05-18 01:42 UTC · model grok-4.3

classification 🌊 nlin.PS physics.opticsquant-ph
keywords hybrid perovskitessuperradianceexciton-phonon interactionsnonlocal NLS equationsoliton stabilityWannier excitonsquantum coherencenonlinear stability analysis
0
0 comments X

The pith

Exciton-phonon interactions preserve stability of superradiant states through a derived 2D nonlocal NLS equation in hybrid perovskites.

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

This paper derives a 2D nonlocal nonlinear Schrödinger equation for the complex polarization of quasi-2D Wannier excitons interacting with LO and acoustic phonons in polar hybrid perovskite crystals. Linear stability analysis of plane-wave solutions, including the superradiant state as a special case, produces explicit criteria for stability. Acoustic phonon interactions lower the intensity of modulationally stable waves relative to the phonon-free case. In the weakly nonlocal limit the equation simplifies to a purely nonlocal form. Numerical solution of the equation in polar coordinates yields a stable fundamental soliton.

Core claim

The system of quasi-2D Wannier excitons interacting with LO and acoustic phonons reduces to a 2D nonlocal NLS equation for the complex polarization. Linear stability analysis of the plane wave solutions establishes stability criteria for the superradiant state. In the weakly nonlocal case the equation becomes purely nonlocal. Interactions with acoustic phonons reduce the intensity of modulationally stable waves. Numerical solution of the 2D nonlocal NLS equation in polar coordinates produces a stable fundamental soliton solution.

What carries the argument

The 2D nonlocal nonlinear Schrödinger equation for the complex polarization, obtained by reducing the exciton-phonon interaction model, which carries the linear stability analysis and supports the fundamental soliton solution.

If this is right

  • Stability criteria apply to the superradiant state because it is a particular plane-wave solution.
  • Acoustic phonon coupling decreases the intensity threshold for modulationally stable waves.
  • The weakly nonlocal regime reduces exactly to a purely nonlocal equation.
  • The fundamental soliton remains stable under the derived dynamics in polar coordinates.

Where Pith is reading between the lines

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

  • Room-temperature macroscopic coherence in perovskites could become practical for quantum technologies if the predicted stability holds under realistic conditions.
  • The same reduction technique may apply to other polar two-dimensional materials with comparable phonon spectra.
  • Adding weak damping terms to the nonlocal equation would provide a direct test of how robust the soliton stability remains.
  • Stable soliton solutions open the possibility of using these structures for nonlinear optical switching in thin films.

Load-bearing premise

The physical system of quasi-2D Wannier excitons interacting with LO and acoustic phonons in polar hybrid perovskite crystals can be accurately reduced to the derived 2D nonlocal NLS equation for the complex polarization without additional damping or higher-order effects that would alter the stability conclusions.

What would settle it

Direct observation of modulation instability or soliton decay in hybrid perovskite samples at intensities and phonon coupling strengths where the stability analysis predicts persistence would falsify the central claim.

Figures

Figures reproduced from arXiv: 2511.03600 by A. A. Gladkij, B. A. Malomed, B. D. Fainberg, N. A. Veretenov, N. N. Rosanov, V. Al. Osipov.

Figure 1
Figure 1. Figure 1: FIG. 1. The parameter of the exciton-phonon interaction [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Modulus of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Square of dimensionless increment ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Modulus of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Function [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Parameter of exciton-acoustic phonon interaction [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Parameter of exciton-acoustic phonon interaction [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Fundamental soliton profile [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Spectrum of ˜γ [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Spectra of ˜γ [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Approximation of [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Spectra of ˜γ [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Spectra of ˜γ [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Spatial distribution of the fundamental soliton amplitude [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
read the original abstract

The use of macroscopic coherent quantum states at room temperature is crucial in modern quantum technologies. In light of recent experiments demonstrating high-temperature superfluorescence in hybrid perovskite thin films, in this work we investigate the stability of the superradiant state concerning exciton-phonon interactions, taking into account the specifics of perovskites. We focused on quasi-2D Wannier excitons interacting with longitudinal optical (LO) phonons in polar crystals, as well as with acoustic phonons. Our study leads to the derivation of nonlinear equations in the coordinate space that govern the exciton wavefunction's coefficient in the single-exciton basis for the lowest exciton state, which translates to the complex-valued polarization. The resulting equations take the form of a 2D nonlocal nonlinear Schrodinger (NLS) equation. We perform a linear stability analysis of the plane wave solutions for the equations in question, which allows us to establish stability criteria. This analysis is particularly important for evaluating the stability of the superradiant state in the considered quasi-2D structures, as the superradiant state represents a specific case of the plane wave solution. In scenarios involving the weakly nonlocal NLS equation, we find that it transitions into a purely nonlocal form. Furthermore, interactions between the exciton and acoustic phonons reduce the intensity of modulationally stable waves compared to the case without such interactions. Our analytical results are corroborated by numerical calculations. We also numerically solve the 2D nonlocal NLS equation in the polar coordinates and obtain its fundamental soliton solution, which is stable.

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 / 1 minor

Summary. The manuscript models quasi-2D Wannier excitons interacting with LO and acoustic phonons in hybrid perovskites, derives a 2D nonlocal nonlinear Schrödinger equation for the complex polarization, performs linear stability analysis on plane-wave solutions to obtain stability criteria for the superradiant state, and numerically constructs a stable fundamental soliton solution in polar coordinates.

Significance. If the conservative reduction holds and the numerical stability is robust, the work supplies concrete stability thresholds and a soliton solution that could help explain room-temperature superfluorescence observations in perovskite films, with direct relevance to coherent quantum states in polar materials.

major comments (2)
  1. The derivation of the 2D nonlocal NLS (model-reduction section) truncates at the nonlocal kernel while omitting higher-order exciton-phonon scattering channels that generate effective damping or loss. Because the central stability criteria and soliton stability are obtained for the closed conservative system, restoring even weak dissipative terms from acoustic-phonon relaxation could cause amplitude decay or radiation on timescales comparable to the modulationally stable regime, directly undermining the reported stability conclusions.
  2. Numerical solution of the fundamental soliton (results section on polar-coordinate integration): no details are given on the discretization scheme, spatial grid, time-stepping method, or the specific perturbation protocol used to test stability. Without these, it is impossible to assess whether the reported stability survives small numerical or physical perturbations.
minor comments (1)
  1. The transition from the weakly nonlocal to purely nonlocal form is stated but not accompanied by an explicit parameter regime or scaling argument that justifies dropping the local term.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript concerning the stability of quantum coherent superradiant states in hybrid perovskites. We address each major comment point by point below, providing clarifications and indicating revisions where appropriate.

read point-by-point responses

  1. Referee: The derivation of the 2D nonlocal NLS (model-reduction section) truncates at the nonlocal kernel while omitting higher-order exciton-phonon scattering channels that generate effective damping or loss. Because the central stability criteria and soliton stability are obtained for the closed conservative system, restoring even weak dissipative terms from acoustic-phonon relaxation could cause amplitude decay or radiation on timescales comparable to the modulationally stable regime, directly undermining the reported stability conclusions.

    Authors: We acknowledge that the derivation presented in the model-reduction section focuses on the conservative dynamics obtained by truncating at the nonlocal kernel derived from the exciton-phonon coupling. Higher-order scattering channels that could introduce damping are indeed omitted, as the model emphasizes the coherent interactions relevant to superradiance. The stability analysis and soliton solution are for this conservative system, which represents a key limiting case. To strengthen the manuscript, we will include an additional paragraph discussing the potential effects of weak dissipation from acoustic phonons, including order-of-magnitude estimates of decay timescales relative to the modulationally stable regime. This will better contextualize the applicability of our stability criteria. revision: partial

  2. Referee: Numerical solution of the fundamental soliton (results section on polar-coordinate integration): no details are given on the discretization scheme, spatial grid, time-stepping method, or the specific perturbation protocol used to test stability. Without these, it is impossible to assess whether the reported stability survives small numerical or physical perturbations.

    Authors: We agree that the numerical methods section lacks sufficient detail for reproducibility. In the revised manuscript, we will provide a comprehensive description of the numerical approach, including the discretization scheme used for the polar-coordinate integration (e.g., finite-difference or pseudospectral method), the spatial grid size and resolution, the time-stepping method (such as the split-step Fourier transform or explicit Runge-Kutta), and the specific perturbation protocol employed to verify the soliton's stability against small perturbations. These additions will enable independent verification of the numerical stability results. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation from standard Hamiltonians to NLS and numerical soliton are independent

full rationale

The paper begins from conventional exciton-phonon Hamiltonians for quasi-2D Wannier excitons interacting with LO and acoustic phonons, reduces them to a 2D nonlocal NLS equation for the complex polarization, performs linear stability analysis on its plane-wave solutions, and numerically obtains a stable fundamental soliton in polar coordinates. These steps are direct computations on the derived model; no parameter is fitted to the target stability result, no self-citation chain bears the central claim, and the soliton existence is not equivalent to the input by construction. The reduction employs standard approximations whose validity is external to the final numerical stability statement, rendering the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the quasi-2D Wannier exciton model with longitudinal optical and acoustic phonon couplings in polar crystals, plus the reduction of the many-body dynamics to a single complex polarization field obeying the nonlocal NLS. No explicit free parameters or invented entities are stated in the abstract.

axioms (2)
  • domain assumption Quasi-2D Wannier excitons in polar hybrid perovskites interact with LO and acoustic phonons via standard Fröhlich-type couplings that can be integrated out to produce a nonlocal nonlinearity.
    Invoked when the authors state they focus on quasi-2D Wannier excitons interacting with LO phonons in polar crystals as well as acoustic phonons.
  • domain assumption The single-exciton basis for the lowest exciton state yields a complex-valued polarization whose dynamics are governed by a closed nonlinear equation.
    Stated when the work leads to nonlinear equations for the exciton wavefunction coefficient in the single-exciton basis.

pith-pipeline@v0.9.0 · 5867 in / 1512 out tokens · 29671 ms · 2026-05-18T01:42:22.466256+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The resulting equations take the form of a 2D nonlocal nonlinear Schrodinger (NLS) equation... We also numerically solve the 2D nonlocal NLS equation in the polar coordinates and obtain its fundamental soliton solution, which is stable.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

  1. [1]

    Dimensional values are ob- tained by multiplying by the characteristic lengthD= 4 p ℏl3 0/(4G 0M ∗l) and characteristic timeτ= p M ∗l3 0/(G 0lℏ), respectively

    Subcritical case The numerical results obtained for a spatially homogeneous initial condition with noise for subcritical case (ρ 0 = 0.5ρcr,0 whereρ cr,0 ≡ρ cr(¯k→0)≃0.01) are shown in Fig.2 in dimensionless coordinates. Dimensional values are ob- tained by multiplying by the characteristic lengthD= 4 p ℏl3 0/(4G 0M ∗l) and characteristic timeτ= p M ∗l3 0...

    work page

  2. [2]

    This allows us to find the value ofkDfor which the increment is maximum for some value of ρ0 > ρ cr,0

    Instability analysis Fig.3 shows the square of the dimensionless increment (λτ)2 as a function of the wave intensityρ0 and dimensionless wave numberkD. This allows us to find the value ofkDfor which the increment is maximum for some value of ρ0 > ρ cr,0. Forρ 0 = 10ρ cr,0 ≃0.1, the maximum increment value is achieved atkD≈0.43. In this case, the value of ...

    work page

  3. [3]

    Fig.4 illustrates the development of instability of a plane wave in the supercritical case

    Modeling the development of instability The numerical results obtained for a spatially homogeneous initial condition with noise for a supercritical case (ρ0 = 10ρcr,0 ≃0.1) are shown in Fig.4 in dimensionless coordinates. Fig.4 illustrates the development of instability of a plane wave in the supercritical case. A plane wave with a noise perturbed amplitu...

    work page

  4. [4]

    High-temperature superfluorescence in methyl ammonium lead iodide,

    G. Findik, M. Biliroglu, D. Seyitliyev, J. Mendes, A. Barrette, H. Ardekani, L. Lei, Q. Dong, F. So, and K. Gundogdu, 2021, “High-temperature superfluorescence in methyl ammonium lead iodide,”Nature Photonics, vol. 15, pp. 676–680

    work page 2021

  5. [5]

    Room-temperature superfluorescence in hybrid perovskites and its origins,

    M. Biliroglu, G. Findik, J. Mendes, D. Seyitliyev, L. Lei, Q. Dong, Y. Mehta, V. V. Temnov, F. So, and K. Gundogdu, 2022, “Room-temperature superfluorescence in hybrid perovskites and its origins,”Nature Photonics, vol. 16, pp. 324–329

    work page 2022

  6. [6]

    Superlattice-induced super- fluorescence in quasi-2d metal halide perovskites,

    A. J. Wildenborg, R. J. Munter, F. Freire-Fernandez, E. T. F. Freitas, and J. Y. Suh, 2025, “Superlattice-induced super- fluorescence in quasi-2d metal halide perovskites,”ACS Photonics

    work page 2025

  7. [7]

    Theory of high-temperature superfluorescence in hybrid perovskite thin films,

    B. D. Fainberg and V. A. Osipov, 2024, “Theory of high-temperature superfluorescence in hybrid perovskite thin films,” J. Chem. Phys., vol. 161, no. 11, p. 114705

    work page 2024

  8. [8]

    Two-dimensional solitons in nonlocal media: A brief review,

    B. A. Malomed, 2022, “Two-dimensional solitons in nonlocal media: A brief review,”Symmetry, vol. 14, p. 1565

    work page 2022

  9. [9]

    Modulational instability in nonlocal nonlinear kerr media,

    W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, 2001, “Modulational instability in nonlocal nonlinear kerr media,”Phys. Rev. E, vol. 64, p. 016612

    work page 2001

  10. [10]

    Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,

    W. Krolikowski, 2004, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,”J. Opt. B: Quantum Semiclass. Opt., vol. 6, pp. S288–S294

    work page 2004

  11. [11]

    Exciton polarons in two-dimensional hybrid metal-halide perovskites,

    A. R. S. Kandada and C. Silva, 2020, “Exciton polarons in two-dimensional hybrid metal-halide perovskites,”J. Phys. Chem. Lett., vol. 11, pp. 3173–3184. 20 FIG. 13. Spectra of ˜γfor ˜Ω = 4 andδm= 1 (a),δm= 2 (b),δm= 3 (c)

    work page 2020

  12. [12]

    Coherent and incoherent states of the radiation field,

    R. J. Glauber, 1963, “Coherent and incoherent states of the radiation field,”Phys. Rev, vol. 131, no. 2, pp. 2766–2788

    work page 1963

  13. [13]

    On the completeness of coherent states generated by binomial distribution,

    J.-M. Sixdeniers and K. A. Penson, 2000, “On the completeness of coherent states generated by binomial distribution,”Journal of Physics A: Mathematical and General, vol. 33, no. 14, pp. 2907–2916. [Online]. Available: https://doi.org/10.1088/0305-4470/33/14/319

    work page doi:10.1088/0305-4470/33/14/319 2000

  14. [14]

    Solitons in quasi-one-dimensional molecular structures,

    A. S. Davydov, 1982, “Solitons in quasi-one-dimensional molecular structures,”Soviet Physics Uspekhi, vol. 25, no. 12, p. 898

    work page 1982

  15. [15]

    Davydov ansatz as an efficient tool for the simulation of nonlinear optical response of molecular aggregates,

    K.-W. Sun, M. F. Gelin, V. Y. Chernyak, and Y. Zhao, 2015, “Davydov ansatz as an efficient tool for the simulation of nonlinear optical response of molecular aggregates,”J. Chem. Phys., vol. 142, p. 212448

    work page 2015

  16. [16]

    Kittel, 1963,Quantum theory of solids

    C. Kittel, 1963,Quantum theory of solids. New York-London: John Wiley and Sons

    work page 1963

  17. [17]

    A. S. Davydov, 1971,Theory of Molecular Excitons. New York: Plenum

    work page 1971

  18. [18]

    V. M. Agranovich, 2009,Excitations in Organic Solids. New York: Oxford University Press

    work page 2009

  19. [19]

    Study of electron-vibrational interaction in molecular aggregates using mean-field theory: From exciton absorption and luminescence to exciton-polariton dispersion in nanofibers,

    B. D. Fainberg, 2019, “Study of electron-vibrational interaction in molecular aggregates using mean-field theory: From exciton absorption and luminescence to exciton-polariton dispersion in nanofibers,”J. Phys. Chem. C, vol. 123, pp. 7366– 7375

    work page 2019

  20. [20]

    Solitons in nonlocal nonlinear media: Exact solutions,

    W. Krolikowski and O. Bang, 2000, “Solitons in nonlocal nonlinear media: Exact solutions,”Phys. Rev. E, vol. 63, p. 016610, 2000

    work page 2000

  21. [21]

    Electrons in lattice fields,

    H. Frohlich, 1954, “Electrons in lattice fields,”Advances in Physics, vol. 3, no. 11, pp. 325–361

    work page 1954

  22. [22]

    R. P. Feynman, 1998,Statistical Mechanics. Boulder, Colorado: Westview press

    work page 1998

  23. [23]

    Singh, 1994,Excitation Energy Transfer in Condensed Matter

    J. Singh, 1994,Excitation Energy Transfer in Condensed Matter. Theory and Applications. New York: Springer Sci- ence+Business Media

    work page 1994

  24. [24]

    Large polarons in lead halide perovskites,

    K. Miyata, D. Meggiolaro, M. T. Trinh, P. P. Joshi, E. Mosconi, S. C. Jones, F. D. Angelis, and X.-Y. Zhu, 2017, “Large polarons in lead halide perovskites,”Sci. Adv., vol. 3, p. e1701217

    work page 2017

  25. [25]

    Subharmonic modulational instabilities,

    W.-R. Sun and B. A. Malomed, 2025, “Subharmonic modulational instabilities,”Phys. Rep., vol. 1139, pp. 1–62

    work page 2025

  26. [26]

    Inversion symmetry and bulk rashba effect in methylammonium lead iodide perovskite single crystals,

    K. Frohna, T. Deshpande, J. Harter, W. Peng, B. A. Barker, J. B. Neaton, S. G. Louie, O. M. Bakr, D. Hsieh, and M. Bernardi, 2018, “Inversion symmetry and bulk rashba effect in methylammonium lead iodide perovskite single crystals,” Nature Communications, vol. 9, p. 1829. 21 FIG. 14. Spatial distribution of the fundamental soliton amplitude| ˜C0(˜x,˜y, t)...

    work page 2018

  27. [27]

    Upper-hybrid solitons and oscillating-two-stream instabilities,

    M. Porkolab and M. V. Goldman, 1976, “Upper-hybrid solitons and oscillating-two-stream instabilities,”Phys. Fluids, vol. 19, pp. 872–881

    work page 1976

  28. [28]

    A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates,

    J. J. Garcia-Ripoll, V. V. Konotop, B. Malomed, and V. M. Perez-Garcia, 2003, “A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates,”Mathematics and Computers in Simulation, vol. 62, pp. 21–30

    work page 2003

  29. [29]

    On the dynamical behavior of an exciton,

    Y. Toyozawa, 1959, “On the dynamical behavior of an exciton,”Progr. Theor. Phys. Suppl., vol. 12, pp. 111–140

    work page 1959

  30. [30]

    Theory of line-shapes of the exciton absorption bands,

    Y. Toyozawa, 1958, “Theory of line-shapes of the exciton absorption bands,”Progr. Theor. Phys., vol. 20, no. 1, pp. 53–81

    work page 1958