Pith. sign in

REVIEW 2 major objections 7 minor 1 cited by

Microscopic Theory of Polariton Group Velocity Renormalization

T0 review · 2 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper derives a parameter-free formula for the lower-polariton group velocity renormalization as phonon-mediated virtual scattering through dark states, and verifies it against quantum-dynamics simulations.

desk verdict A parameter-free microscopic theory of polariton group velocity renormalization that is probably right in the weak-coupling band-like regime, with an unproven transport premise and some reproducibility gaps. read the letter →

arxiv 2411.08288 v2 pith:3T6MBDDB submitted 2024-11-13 quant-ph cond-mat.mes-hall

Wenxiang Ying , Benjamin X. K. Chng , Milan Delor , Pengfei Huo This is my paper · ORCID
classification quant-phcond-mat.mes-hall PACS 71.36.+c71.38.-k42.50.Pq
keywords polaritontransportgroupvelocityrenormalizationdarkstatesHopfieldcoefficientssecond-orderself-energyfinite-temperatureGreen'sfunctionexciton-phononcouplingcavityquantumelectrodynamics
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

Cavity exciton-polaritons can travel ballistically over long distances, but phonons reduce their speed in a way that no microscopic theory had predicted. This paper derives that reduction from first principles using a finite-temperature Green's function treatment of the generalized Holstein-Tavis-Cummings model. The central result is a parameter-free formula for the lower-polariton group velocity renormalization $\Delta v_{g,-}$: it is the derivative of a second-order self-energy generated by phonon-mediated virtual transitions from the lower polariton into the dark-state manifold and back (Eqs. 18 and 20). The formula predicts $|\Delta v_{g,-}| \propto \lambda$ at weak exciton-phonon coupling and $\Delta v_{g,-} \propto T$ at high temperature, and mixed quantum-classical simulations agree quantitatively in that regime. Because there is no fitted constant, the theory supersedes the thermally activated scattering model, whose free parameter cannot reproduce the temperature dependence.

What carries the argument

The machinery is the finite-temperature polariton Green's function solved through the Dyson equation, with the phonon-mediated self-energy taken at second order. The object doing the work is the dark-state manifold as a virtual intermediate: the sum over the $N-M$ dark states collapses to a factor $(N-M)f(\omega_0)$ that cancels the $1/N$ normalization of the phonon mode, leaving the matter fraction $|C_k|^2 = \sin^2\Theta_k$ and the dark-LP energy gap $\Delta\omega_{-k} = \omega_0 - \omega_{-k}$ as the controlling parameters. The second-order polarizability $\Xi_{-k,0}(\omega_\alpha)$ in Eqs. 17 and 19 is the temperature-dependent Raman-type polarizability for the phonon-mediated transition, and its $k_\parallel$ derivative in Eq. 20 converts the band renormalization into a group velocity renormalization.

What would settle it

Measure the lower-polariton group velocity as a function of reorganization energy $\lambda$ at fixed temperature and in-plane momentum: Eq. 20 predicts a straight line through the bare value whose slope is fixed by the phonon spectral density and Hopfield coefficient. A nonlinear $\lambda$ dependence at small $\lambda$, or a high-temperature dependence that saturates like $1/(1+e^{-\beta\hbar\Delta\omega_{-k}})$ instead of growing linearly in $T$, would falsify the central claim.

Watch

Extended reading notes

Core claim

The paper's claim is that the observed slowdown of lower-polariton transport is a band-structure effect, not primarily a transient dynamical effect. In the finite-temperature Green's function formalism, the renormalized lower-polariton energy $E_{-k}$ is the bare energy plus the real part of the second-order phonon self-energy, and the renormalized group velocity is $\tilde v_{g,-} = (1/\hbar)\,dE_{-k}/dk_\parallel$ (Eq. 13). The dominant contribution to the self-energy comes from the $N-M$ dark exciton states, which act as virtual intermediate states in a super-exchange process $|-,k\rangle \to |D\rangle \to |-,k\rangle$; the dark states need not be populated, and for large detuning they remain spectroscopically dark. The resulting analytic expression (Eq. 18, with the $\eta\to 0$ form in Eq. 20) is the $k_\parallel$-derivative of a Hopfield-weighted sum over phonon modes of the Raman-type polarizability $\Xi_{-k,0}(\omega_\alpha)$, controlled by the LP-dark gap $\Delta\omega_{-k}$ and the Bose-Einstein occupation $n_\alpha$. The paper claims this gives $|\Delta v_{g,-}| \propto \lambda$ at weak coupling and $\Delta v_{g,-} \propto T$ at high temperature, and that the simulations confirm the scaling quantitatively up to $\lambda \sim k_BT$, beyond which perturbation theory degrades but the trend survives.

Load-bearing premise

The load-bearing assumption is that a propagating polariton wavepacket remains a well-defined quasiparticle in a single band, so its speed is the derivative of the equilibrium renormalized energy; the paper assumes this band-like regime rather than deriving it from the transport dynamics.

Editorial extensions

If this is right

  • Dark states act as virtual intermediates, so the slowdown persists at large light-matter detuning even though the dark states are never populated.
  • In the band-like regime the long-time group velocity is set by the phonon-renormalized band, so transient non-equilibrium localization does not control the asymptotic speed.
  • The renormalization grows linearly with reorganization energy at weak coupling and linearly with temperature when $\hbar\omega_\alpha \ll k_BT$, providing a clear experimental signature that distinguishes this mechanism from thermally activated scattering.
  • Because the theory has no free parameters, a measurement of $\Delta v_{g,-}$ at one temperature and coupling fixes the full predicted curve, up to the perturbative breakdown at large $\lambda$.

Reading between the lines

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

  • The predicted $1/\Delta\omega_{-k}$ dependence suggests that scanning the cavity detuning would map the influence of the dark-state manifold on transport, a direct experimental test the paper does not perform.
  • If the band-like assumption fails at short times, wavefront velocities measured before the self-energy is established should deviate from Eq. 20, so ultrafast imaging could locate the crossover between transient and band-like transport.
  • Applying the same second-order self-energy to upper polaritons or to dispersive dark bands would replace the flat $(N-M)f(\omega_0)$ sum with a density of states; the paper notes this extension is feasible but does not carry it out.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. The paper develops a finite-temperature Green's function theory for the group velocity renormalization of lower polaritons in a generalized Holstein–Tavis–Cummings model. Using the Fan–Migdal self-energy, the authors derive an analytic expression (Eqs. 16–20) for Δv_g as the derivative of the second-order phonon-induced polariton energy shift. They argue that the dominant contribution comes from virtual transitions from the LP to the dark-state manifold and back, a process they term super-exchange. The theory predicts Δv_g ∝ λ in the weak-coupling regime and a linear-in-T dependence at high temperature, and these predictions are compared against Ehrenfest mixed quantum-classical dynamics simulations with no adjustable parameters. The paper also contrasts the new theory with the phenomenological thermally-activated-scattering model, showing that the latter fails to reproduce the correct temperature dependence.

Significance. If correct, this work provides the first parameter-free microscopic derivation of polariton group velocity renormalization, with falsifiable scaling predictions in λ, T, and the Hopfield coefficient. The explicit mechanism of dark-state-mediated super-exchange is conceptually new and goes beyond the phenomenological thermally activated scattering picture. The paper uses a standard diagrammatic framework, derives closed-form expressions, and tests them against independent Ehrenfest dynamics using the same input parameters; this is a genuine zero-free-parameter comparison, and the authors are candid about the theory's weak-coupling regime of validity. The main weaknesses are the assumed identification of the transport velocity with the equilibrium band derivative and the lack of a direct numerical check of the dark-state dominance, both of which affect the interpretation of the central result.

major comments (2)
  1. [Theory, Eq. (13)] The identification of the observable polariton group velocity with the derivative of the equilibrium renormalized band, \tilde v_g,± = (1/ℏ)dE±k/dk_∥, is assumed rather than derived. The paper restricts to 'the band-like transport regime' but gives no quantitative criterion (e.g., wavepacket width relative to the polaron mean free path, or the spectral linewidth relative to the band curvature) that guarantees the long-time wavepacket velocity equals this band derivative. Phonon-induced transient localization, as proposed in Ref. 4, is a competing mechanism that could make the measured velocity differ from the equilibrium-band derivative. The agreement with Ehrenfest dynamics in Fig. 2 is suggestive, but Ehrenfest is a mean-field approximation that can misestimate decoherence and localization, so it does not conclusively validate the mapping. This point is load-bearing because the λ and T scaling laws are properties of the band derivative, not of an independently derived transport velocity. Please derive the mapping from a wavepacket or Kubo-type transport calculation, or state and test an explicit condition for its validity.
  2. [Mechanistic Picture, Eqs. (16)–(18)] The claim that the dark-state manifold dominates the renormalization is argued solely from the state count (N − M ≫ 2M). The numerical results in Fig. 2 are stated to use Eq. (16), which contains all intermediate bands, whereas the closed-form expression Eq. (18) and the mechanistic discussion retain only the dark-state channel. The paper does not show a numerical or analytical comparison between the full sum and the dark-only approximation. This matters because the LP intermediate channel can have small energy denominators near degeneracy, potentially compensating for the 1/N suppression. Since the central mechanistic conclusion—that the effect is a phonon-mediated super-exchange through the dark states—rests on this dominance, please provide a direct comparison of the full Eq. (16) with Eq. (18) for the parameters of Fig. 2, or a more explicit proof that the bright-state channels contribute at most of order M/N even in the presence of near-resonant denominators.
minor comments (7)
  1. [Abstract and Fig. 2] The abstract states 'quantitative agreement' with simulations, but the text (Fig. 2 caption and the discussion near the end of 'Numerical Results') qualifies the agreement as semi-quantitative for larger λ and matter fractions. Please align the abstract with the actual degree of agreement.
  2. [Theory, Eqs. (16)–(18)] The 'no free parameter' claim is overstated: the theory uses the Drude–Lorentz characteristic frequency ωf and the broadening η as inputs. Since these are not fitted to the simulations, 'no fitting parameters' would be more precise.
  3. [Theory, paragraph preceding Eq. (18)] The sentence 'the N − M factor will cancel with 1/N in Eq. 17' appears to refer to Eq. 16 rather than Eq. 17; please correct the citation.
  4. [Methods, Simulation Details] The statement 'N = 10^4 molecules and M = 10^2 cavity modes, keeping the ratio of N/M ≈ 35' is arithmetically inconsistent because 10^4/10^2 = 100. Please correct the ratio or the numbers.
  5. [References, Ref. [25]] Reference [25] contains an unresolved placeholder '[ ? ]' in the parenthetical estimate of typical experimental N/M values; please provide the intended citation or remove the placeholder.
  6. [Theory, Eqs. (12) and (16)] Eq. (12) defines the self-consistent renormalized energy, while Eq. (16) is a second-order on-shell approximation evaluated at the bare frequency. State explicitly that Eq. (16) is the leading-order result and that the self-energy in Eq. (17) is evaluated at the bare polariton frequencies.
  7. [Numerical Results, temperature dependence] The phrase 'the modification of the polariton band structure (or group velocity) is proportional to T' is not literally correct because Eq. (20) contains a T-independent term from the 1 in (2nα + 1). Please rephrase as 'linear in T' in the high-temperature limit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the renormalized group velocity is an analytic perturbative consequence of the stated Hamiltonian, and the Ehrenfest comparison is an independent numerical check.

full rationale

The paper's central derivation starts from the generalized Holstein-Tavis-Cummings Hamiltonian and obtains the renormalized polariton band via the finite-temperature Dyson equation and the Fan-Migdal self-energy (Eqs. 9-17). The final expressions for the LP group velocity renormalization (Eqs. 18 and 20) follow from evaluating this self-energy for the dark-state manifold; no fitted parameters appear, and the claimed scaling with reorganization energy λ and temperature T follows directly from c_α^2 and the Bose-Einstein factors n_α in Eq. 15. The numerical comparison uses Ehrenfest mixed quantum-classical dynamics that propagate an actual polariton wavepacket and track its wavefront, so the simulated group velocity is not constructed from Eq. 13 by definition. The self-citations to Refs. [4] and [19] are used to motivate the hypothesis that the self-energy correction is the dominant cause of renormalization and to specify the simulation methodology, but they do not supply the derivation themselves. The identification of the measured group velocity with the derivative of the renormalized equilibrium band (Eq. 13) is an explicit modeling assumption, not an input secretly reused as an output; any concern about transient localization is a validity question, not a circularity. Therefore the derivation is self-contained and no circular step can be exhibited.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The theory is a parameter-free perturbative derivation from the GHTC Hamiltonian; no free constants are fitted to the simulation data. However, the model itself embodies several domain assumptions, and the numerical comparison requires a spectral density shape with an unspecified characteristic frequency. The 'no free parameter' claim refers to the absence of fitted constants, not the absence of model assumptions.

free parameters (2)
  • Drude-Lorentz characteristic frequency ωf
    The spectral density J(ω)=2λωf ω/(ω^2+ωf^2) is used in Methods, but the main text does not state the value of ωf used in Fig. 2, making exact reproduction of the theoretical curves impossible from the main text alone.
  • Broadening parameter η = 1 meV
    Introduced ad hoc in Eq. 17 as an infinitesimal imaginary part; set to 1 meV in the numerical evaluation of Eq. 16 for convergence.
assumptions (4)
  • domain assumption The GHTC Hamiltonian accurately models cavity exciton-polaritons in molecular systems (identical two-level excitons, M cavity modes, independent harmonic phonon baths).
    Introduced in the Model System section; real systems with disorder, anharmonicity, or non-identical molecules may not follow the predictions.
  • domain assumption Weak exciton-phonon coupling: the Fan-Migdal first-order self-energy (Eq. 14) captures the leading band renormalization.
    The paper acknowledges in Fig. 2c that the theory deviates from simulations at larger λ, entering the non-perturbative regime.
  • domain assumption Band-like transport: the renormalized single-particle energy determines the group velocity via dE/dk∥ (Eq. 13).
    This is the load-bearing premise; the paper restricts to the band-like transport regime but does not derive it.
  • domain assumption Dark states dominate the self-energy sum and can be approximated as a flat band at energy ℏω0 (N-M >> 2M).
    Used between Eqs. 17 and 18 to reduce the sum over k' to (N-M)f(ω0), with the 1/N factor cancelling; if N/M is not small, the analytic expression changes.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Microscopic Theory of Polariton Group Velocity Renormalization." pith.science (2026). https://pith.science/paper/3T6MBDDB

@misc{pith2026241108288,
  author       = {Pith},
  title        = {Pith review of: Microscopic Theory of Polariton Group Velocity Renormalization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3T6MBDDB}},
  note         = {Machine review of arXiv:2411.08288}
}
abstract

Cavity exciton-polaritons exhibit ballistic transport and can achieve a distance of 100 $\mu $m in one picosecond. This ballistic transport significantly enhances mobility compared to that of bare excitons, which often move diffusively and become the bottleneck for energy conversion and transfer devices. Despite being robustly reproduced in experiments and simulations, there is no comprehensive microscopic theory addressing the group velocity of polariton transport, and its renormalization due to phonon scattering while still preserving this ballistic behavior. In this work, we develop a microscopic theory to describe the group velocity renormalization using a finite-temperature Green's function approach. Utilizing the generalized Holstein-Tavis-Cummings Hamiltonian, we analytically derive an expression for the group velocity renormalization and find that it is caused by phonon-mediated transitions from the lower polariton (LP) states to the dark states, then scattering from dark states back to LP. The dark states do not have to be populated in this process, serving as the virtual state for super-exchange (especially true for a large light-matter detuning). The theory predicts that the magnitude of group velocity renormalization scales linearly with the phonon bath reorganization energy under weak coupling conditions (perturbative regime for exciton-phonon coupling) and also linearly depends on the temperature in the high-temperature regime. These predictions are numerically verified using quantum dynamics simulations, demonstrating quantitative agreement. Our findings provide theoretical insights and a predictive analytical framework that advance the understanding and design of cavity-modified semiconductors and molecular ensembles, opening new avenues for engineered polaritonic devices.

Figures

Figures reproduced from arXiv: 2411.08288 by the authors.

Figure 1
Figure 1. Without coupling to phonons, the polariton ex- [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Static disorder-induced renormalization of polariton group velocity

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Static energetic disorder slows lower and upper polaritons, but for realistic organic microcavities the effect is too small to explain observed slowdown, pointing to phonon scattering as the dominant mechanism.

Reference graph

Works this paper leans on

39 extracted references · 28 canonical work pages · cited by 1 Pith paper

  1. [1]

    We present a schematic illustration of the model sys- tem above, as well as the polariton band structure, in Fig. 1. Without coupling to phonons, the polariton ex- 3 hibits band-like transport characterized by the group ve- locity vg,±(k∥) = dω±k/dk∥, (6) where the k∥-dependence of ω±k is carried by ωk via Eq. 2. The bath Hamiltonian ˆhB describes the nuc...

    work page

  2. [2]

    S. Hou, M. Khatoniar, K. Ding, Y. Qu, A. Napolov, V. M. Menon, and S. R. Forrest, Ultralong-range energy trans- port in a disordered organic semiconductor at room tem- perature via coherent exciton-polariton propagation, Ad- vanced Materials 32, 10.1002/adma.202002127 (2020)

    doi:10.1002/adma.202002127 2020

  3. [3]

    A. M. Berghuis, R. H. Tichauer, L. M. de Jong, I. Sokolovskii, P. Bai, M. Ramezani, S. Murai, G. Groen- hof, and J. G´ omez Rivas, Controlling exciton propagation in organic crystals through strong coupling to plasmonic nanoparticle arrays, ACS photonics 9, 2263 (2022)

    work page 2022

  4. [4]

    Pandya, A

    R. Pandya, A. Ashoka, K. Georgiou, J. Sung, R. Jayaprakash, S. Renken, L. Gai, Z. Shen, A. Rao, and A. J. Musser, Tuning the coherent propagation of organic exciton-polaritons through dark state delocaliza- tion, Advanced Science 9, 2105569 (2022)

    work page 2022

  5. [5]

    D. Xu, A. Mandal, J. M. Baxter, S. W. Cheng, I. Lee, H. Su, S. Liu, D. R. Reichman, and M. Delor, Ultrafast imaging of polariton propagation and interactions, Na- ture Communications 14, 681–708 (2023)

    work page 2023

  6. [6]

    S. W. Cheng, D. Xu, H. Su, J. M. Baxter, L. N. Holtz- man, K. Watanabe, T. Taniguchi, J. C. Hone, K. Bar- mak, and M. Delor, Optical imaging of ultrafast phonon- polariton propagation through an excitonic sensor, Nano Letters 23, 9936 (2023)

    work page 2023

  7. [7]

    Balasubrahmaniyam, A

    M. Balasubrahmaniyam, A. Simkhovich, A. Golombek, G. Sandik, G. Ankonina, and T. Schwartz, From en- hanced diffusion to ultrafast ballistic motion of hy- brid light–matter excitations, Nature Materials 22, 338 (2023)

    work page 2023

  8. [8]

    Sandik, J

    G. Sandik, J. Feist, F. J. Garc ´ ıa-Vidal, and T. Schwartz, Cavity-enhanced energy transport in molecular systems, Nature Materials 10.1038/s41563-024-01962-5 (2024)

    doi:10.1038/s41563-024-01962-5 2024

Show all 39 references
  1. [9]

    D. Xu, A. Mandal, J. M. Baxter, S.-W. Cheng, I. Lee, H. Su, S. Liu, D. R. Reichman, and M. Delor, Ultrafast imaging of polariton propagation and interactions, Na- ture Communications 14, 3881 (2023)

    2023

  2. [10]

    M. C. Gather, A. K¨ ohnen, and K. Meerholz, White or- ganic light-emitting diodes, Advanced Materials 23, 233 (2011)

    2011

  3. [11]

    Reineke, F

    S. Reineke, F. Lindner, G. Schwartz, N. Seidler, K. Walzer, B. L¨ ussem, and K. Leo, White organic light- emitting diodes with fluorescent tube efficiency, Nature 459, 234 (2009)

    2009

  4. [12]

    Reineke, M

    S. Reineke, M. Thomschke, B. L¨ ussem, and K. Leo, White organic light-emitting diodes: Status and perspec- tive, Reviews of Modern Physics 85, 1245 (2013)

    2013

  5. [13]

    Schachenmayer, C

    J. Schachenmayer, C. Genes, E. Tignone, and G. Pupillo, Cavity-enhanced transport of excitons, Phys. Rev. Lett. 114, 196403 (2015)

    2015

  6. [14]

    Zhou, H.-T

    Z. Zhou, H.-T. Chen, M. Sukharev, J. E. Subotnik, and A. Nitzan, Nature of polariton transport in a fabry-perot cavity, Phys. Rev. A 109, 033717 (2024)

    2024

  7. [15]

    Suyabatmaz and R

    E. Suyabatmaz and R. F. Ribeiro, Vibrational polariton transport in disordered media, The Journal of Chemical Physics 159, 034701 (2023)

    2023

  8. [16]

    G. J. R. Aroeira, K. T. Kairys, and R. F. Ribeiro, Coher- ent transient exciton transport in disordered polaritonic wires, Nanophotonics 13, 2553 (2024)

    2024

  9. [17]

    Engelhardt and J

    G. Engelhardt and J. Cao, Polariton localization and dispersion properties of disordered quantum emitters in multimode microcavities, Phys. Rev. Lett. 130, 213602 (2023)

    2023

  10. [18]

    Tutunnikov, M

    I. Tutunnikov, M. Qutubuddin, H. R. Sadeghpour, and J. Cao, Characterization of polariton dynamics in a multimode cavity: Noise-enhanced ballistic expansion (2024), arXiv:2410.11051 [physics.optics]

    2024 arXiv

  11. [19]

    Sokolovskii, R

    I. Sokolovskii, R. H. Tichauer, D. Morozov, J. Feist, and G. Groenhof, Multi-scale molecular dynamics simu- 9 lations of enhanced energy transfer in organic molecules under strong coupling, Nature Communications 14, 6613 (2023)

    2023

  12. [21]

    R. H. Tichauer, I. Sokolovskii, and G. Groenhof, Tuning the coherent propagation of organic exciton-polaritons through the cavity q-factor, Advanced Science 10, 2302650 (2023)

    2023

  13. [22]

    Herrera and F

    F. Herrera and F. C. Spano, Theory of nanoscale organic cavities: The essential role of vibration-photon dressed states, ACS photonics 5, 65 (2018)

    2018

  14. [23]

    L. Qiu, A. Mandal, O. Morshed, M. T. Meidenbauer, W. Girten, P. Huo, A. N. Vamivakas, and T. D. Krauss, Molecular polaritons generated from strong coupling be- tween cdse nanoplatelets and a dielectric optical cavity, J. Phys. Chem. Lett. 12, 5030 (2021)

    2021

  15. [24]

    Mandal, M

    A. Mandal, M. A. Taylor, B. M. Weight, E. R. Koessler, X. Li, and P. Huo, Theoretical advances in polariton chemistry and molecular cavity quantum electrodynam- ics, Chem. Rev. 123, 9786 (2023)

    2023

  16. [25]

    Taylor, A

    M. Taylor, A. Mandal, and P. Huo, Light-matter inter- action hamiltonians in cavity quantum electrodynamics, ChemRxiv , 10.26434/chemrxiv (2024)

    2024 doi

  17. [26]

    Typically, one estimates N/M ∼106 − 109 for systems used in experiments [ ? ]

  18. [27]

    Caldeira and A

    A. Caldeira and A. Leggett, Quantum tunnelling in a dissipative system, Annals of Physics 149, 374 (1983)

    1983

  19. [28]

    Nitzan, Chemical Dynamics in Condensed Phases (Oxford, New York, 2006)

    A. Nitzan, Chemical Dynamics in Condensed Phases (Oxford, New York, 2006)

    2006

  20. [29]

    H. Deng, H. Haug, and Y. Yamamoto, Exciton-polariton bose-einstein condensation, Rev. Mod. Phys. 82, 1489 (2010)

    2010

  21. [30]

    B. X. K. Chng, W. Ying, Y. Lai, A. N. Vamivakas, S. T. Cundiff, T. D. Krauss, and P. Huo, Mechanism of molec- ular polariton decoherence in the collective light–matter couplings regime, The Journal of Physical Chemistry Let- ters 15, 11773 (2024)

    2024

  22. [31]

    G. D. Mahan, Many-Particle Physics, 3rd Ed.(Springer New York, NY, 2000)

    2000

  23. [32]

    Giustino, Electron-phonon interactions from first prin- ciples, Rev

    F. Giustino, Electron-phonon interactions from first prin- ciples, Rev. Mod. Phys. 89, 015003 (2017)

    2017

  24. [33]

    P. J. Robinson, I. S. Dunn, and D. R. Reichman, Cumu- lant methods for electron-phonon problems. i. perturba- tive expansions, Phys. Rev. B 105, 224304 (2022)

    2022

  25. [34]

    P. J. Robinson, I. S. Dunn, and D. R. Reichman, Cu- mulant methods for electron-phonon problems. ii. the self-consistent cumulant expansion, Phys. Rev. B 105, 224305 (2022)

    2022

  26. [35]

    H. A. Kramers and W. Heisenberg, ¨Uber die streuung von strahlung durch atome, Z. Phys. 31, 681–708 (1925)

    1925

  27. [36]

    P. A. M. Dirac, The quantum theory of the emission and absorption of radiation, Proc. R. Soc. Lond. A. 114, 243–265 (1927)

    1927

  28. [37]

    P. A. M. Dirac, The quantum theory of dispersion, Proc. R. Soc. Lond. A. 114, 710–728 (1927)

    1927

  29. [38]

    D. J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective (University Science Book, 2006)

    2006

  30. [39]

    Bose and N

    A. Bose and N. Makri, Non-equilibrium reactive flux: A unified framework for slow and fast reaction kinetics, The Journal of Chemical Physics 147, 152723 (2017)

    2017

  31. [40]

    D. Hu, B. Chng, W. Ying, and P. Huo, Trajectory- based non-adiabatic simulations of the polariton re- laxation dynamics, ChemRxiv 10.26434/chemrxiv-2024- t818f (2024)

    2024 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.