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arxiv: 2604.18456 · v1 · submitted 2026-04-20 · 🪐 quant-ph · physics.chem-ph

Disorder-induced non-Gaussian states in large ensembles of cavity-coupled molecules

R. Schwengelbeck , M. Pandini , R. Daraban , J. Schachenmayer This is my paper

Pith reviewed 2026-05-10 05:31 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph
keywords polaritonic chemistryHolstein-Tavis-Cummings modelnon-Gaussian statesdisordervibrational dynamicsmatrix product statessemiclassical approximationscavity quantum electrodynamics
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The pith

Disorder induces non-Gaussian vibrational states in large ensembles of cavity-coupled molecules

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

The paper examines vibrational dynamics in a model of molecules under collective strong coupling to a cavity. In the Holstein-Tavis-Cummings framework with incoherent single-photon excitation, disorder rapidly creates non-Gaussian states in the vibrational modes of individual molecules. These non-Gaussian features persist when the ensemble size grows, so the nuclear wave packets cannot be treated as thermal distributions. Exact simulations further show that standard semiclassical methods either require unrealistically large sizes or miss the non-Gaussian character entirely.

Core claim

In the Holstein-Tavis-Cummings model under incoherent photon excitation, disorder leads to non-Gaussian states of vibrational modes on short time scales at the single-molecule level. This effect remains robust for larger molecule numbers, implying that nuclear wave packets cannot be effectively described by thermal states. Exact matrix product state simulations demonstrate that the Ehrenfest approximation reproduces ensemble-averaged observables only for very large system sizes, while the truncated Wigner approximation fails to capture the non-Gaussian effects.

What carries the argument

Disorder within the incoherently excited Holstein-Tavis-Cummings model, tracked through exact matrix product state simulations that expose non-Gaussian vibrational dynamics under collective electronic strong coupling.

If this is right

  • Nuclear wave packets in cavity-coupled systems deviate from thermal states because of disorder-induced non-Gaussianity.
  • The Ehrenfest approximation reproduces ensemble-averaged observables only when molecule numbers become very large.
  • Truncated Wigner simulations miss the non-Gaussian vibrational features generated by disorder.
  • Disorder and genuine quantum effects must be retained when modeling cavity-modified nuclear dynamics.

Where Pith is reading between the lines

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

  • Real experiments may be able to tune disorder to produce desired non-Gaussian vibrational states for reaction control.
  • Polaritonic chemistry models will need explicit disorder terms rather than mean-field or thermal averages.
  • Similar non-Gaussian robustness could appear in other disordered vibronic systems beyond cavity settings.

Load-bearing premise

The specific form of disorder and the incoherent single-photon excitation chosen in the Holstein-Tavis-Cummings toy model are representative of the physics in real polaritonic chemistry experiments.

What would settle it

Spectroscopic measurement of vibrational state distributions in cavity-coupled molecules with controlled disorder, testing whether single-molecule or ensemble wave packets fit thermal distributions or exhibit clear non-Gaussian signatures.

Figures

Figures reproduced from arXiv: 2604.18456 by J. Schachenmayer, M. Pandini, R. Daraban, R. Schwengelbeck.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a). We point out that our numerical calculations are outside the perturbative regime with W = 0.5gc. Furthermore, the perturbative results from [20, 21, 23] rely on a uniform box distribution with εi ∈ [−W/2,W/2] that excludes the tails of the normal disorder distribution considered here. We consider the numerically found non-perturbative scaling of δ[ ˆξ1] ∼ const. in [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 4
Figure 4. Figure 4: , we conclude that this entropy can contribute to a more thermal behavior. However, importantly, we do find that the density matrices on the short time scale still remain significantly different from ˆρth. So far we have examined the overlap of the density matrix with a thermal state at fixed inverse temperature βR. However, it could also be the case that the time￾dependent states resemble thermal states a… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

We analyze vibrational dynamics in a toy model for polaritonic chemistry under collective electronic strong coupling. In a Holstein-Tavis-Cummings model, incoherently excited by a photon, we show that disorder leads to non-Gaussian states of vibrational modes on short time scales at the single-molecule level. Using exact matrix product state simulations, we demonstrate that this effect can remain robust for larger molecule numbers, implying that nuclear wave packets cannot be effectively described by thermal states. Furthermore, we compare simulations of the exact quantum dynamics with semiclassical approximations. We find that the Ehrenfest approximation can only well reproduce ensemble-averaged observables for very large system sizes. Also simulations in the truncated Wigner approximation fail to capture the non-Gaussian effects. Our work highlights the importance of disorder and genuine quantum effects in cavity-modified nuclear dynamics in polaritonic chemistry.

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

3 major / 3 minor

Summary. The manuscript analyzes vibrational dynamics in a disordered Holstein-Tavis-Cummings toy model for polaritonic chemistry under collective strong coupling. It claims that static disorder, combined with incoherent single-photon excitation, generates non-Gaussian states in the vibrational modes at the single-molecule level on short timescales. Exact matrix product state simulations are used to show that this non-Gaussianity remains robust as the number of molecules N increases. The work further compares the exact dynamics to the Ehrenfest and truncated Wigner semiclassical approximations, finding that Ehrenfest reproduces ensemble-averaged observables only at very large N while both approximations fail to capture the non-Gaussian features.

Significance. If the numerical findings hold, the results are significant for polaritonic chemistry because they indicate that nuclear wave packets cannot be reliably approximated as thermal states even in large ensembles when disorder is present. The exact MPS benchmarks against semiclassical methods provide a concrete test of their limitations. The demonstration of size-robust non-Gaussianity is a strength, as is the focus on genuine quantum effects beyond mean-field treatments.

major comments (3)
  1. [§4] §4 (MPS results for large N): The central claim of robustness of non-Gaussianity to increasing molecule number rests on MPS simulations, yet no convergence data with respect to bond dimension, truncation error, or time-step size are reported; without these, it is impossible to verify that the observed single-molecule reduced density matrix features survive the large-N limit.
  2. [§5] §5 (semiclassical comparisons): The statement that the Ehrenfest approximation reproduces ensemble-averaged observables for very large system sizes is presented without a corresponding analysis of whether it preserves or erases the non-Gaussian character of the single-molecule vibrational reduced density matrix; this comparison is load-bearing for the claim that semiclassical methods are inadequate.
  3. [Introduction] Introduction and abstract: The broader implication that the results inform real polaritonic chemistry experiments relies on the specific choice of static diagonal disorder and incoherent excitation; no sensitivity analysis is provided for coherent driving (standard in experiments) or additional fluctuations, creating a correctness-risk concern for the claimed experimental relevance.
minor comments (3)
  1. [Model section] The precise functional form and parameter values of the disorder distribution should be stated explicitly in the model section rather than referenced only by name.
  2. Figure captions would benefit from listing all numerical parameters (coupling strengths, disorder width, photon frequency) used in each panel.
  3. A short paragraph clarifying the difference between ensemble-averaged and single-molecule observables would improve readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions will be made to improve clarity, support, and scope.

read point-by-point responses

  1. Referee: [§4] §4 (MPS results for large N): The central claim of robustness of non-Gaussianity to increasing molecule number rests on MPS simulations, yet no convergence data with respect to bond dimension, truncation error, or time-step size are reported; without these, it is impossible to verify that the observed single-molecule reduced density matrix features survive the large-N limit.

    Authors: We agree that explicit convergence data are necessary to substantiate the robustness claim for the MPS results in the large-N regime. In the revised manuscript we will add a dedicated subsection or supplementary figure panel reporting the dependence of the key non-Gaussianity measures (e.g., higher-order moments or negativity of the Wigner function) on bond dimension, truncation error, and time-step size for representative values of N, including the largest systems considered. These checks will confirm that the reported single-molecule features remain stable within the chosen numerical tolerances. revision: yes

  2. Referee: [§5] §5 (semiclassical comparisons): The statement that the Ehrenfest approximation reproduces ensemble-averaged observables for very large system sizes is presented without a corresponding analysis of whether it preserves or erases the non-Gaussian character of the single-molecule vibrational reduced density matrix; this comparison is load-bearing for the claim that semiclassical methods are inadequate.

    Authors: The referee is correct that the current comparison emphasizes ensemble-averaged observables but does not directly quantify the single-molecule vibrational reduced density matrix under Ehrenfest dynamics at large N. We will revise §5 to include this analysis: we will compute the same non-Gaussianity diagnostics for the Ehrenfest trajectories and show that the vibrational states remain Gaussian (or become more Gaussian) even when ensemble averages converge, in contrast to the exact MPS results. This addition will strengthen the argument that semiclassical methods fail to capture the essential quantum features. revision: yes

  3. Referee: [Introduction] Introduction and abstract: The broader implication that the results inform real polaritonic chemistry experiments relies on the specific choice of static diagonal disorder and incoherent excitation; no sensitivity analysis is provided for coherent driving (standard in experiments) or additional fluctuations, creating a correctness-risk concern for the claimed experimental relevance.

    Authors: We acknowledge that the experimental relevance is model-dependent. The static-disorder and incoherent-excitation setting was chosen to isolate the disorder-induced mechanism in a minimal toy model. In the revised introduction and abstract we will explicitly state the scope of the model, add a short discussion of expected behavior under coherent driving (noting that weak coherent drives with dephasing may preserve similar short-time non-Gaussianity), and indicate that dynamic disorder or other fluctuations lie beyond the present study. A full sensitivity analysis would require substantial additional simulations; we therefore treat this as a limitation to be addressed in future work rather than a claim of broad experimental applicability. revision: partial

Circularity Check

0 steps flagged

Direct MPS simulation of defined HTC Hamiltonian with disorder yields non-Gaussianity without circular reduction

full rationale

The paper derives its claims exclusively from numerical integration of the time-dependent Schrödinger equation for an explicitly stated Holstein-Tavis-Cummings Hamiltonian plus static disorder and an incoherent single-photon excitation protocol. Matrix-product-state results for vibrational reduced density matrices are computed outputs, not inputs that are later renamed as predictions. No parameters are fitted to data and then re-predicted; no self-citation chain supplies a uniqueness theorem or ansatz that the present work merely renames; the non-Gaussian character is an observed dynamical feature inside the model, not presupposed by its definition. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities beyond the standard Holstein-Tavis-Cummings Hamiltonian and the assumption of a particular disorder distribution.

pith-pipeline@v0.9.0 · 5452 in / 1005 out tokens · 35785 ms · 2026-05-10T05:31:55.693135+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    Matrix product states MPS are a well established numerical technique for computing the quantum dynamics of weakly entangled one-dimensional many-body systems [47, 48]. Their efficiency comes from a local, low-rank approximation of the full state, constructed by truncating the Schmidt decomposition across each bond to a large-enough bond dimensionχ. We evo...

    work page

  2. [2]

    Ehrenfest mean-field

    Ehrenfest mean-field By “Ehrenfest mean-field” we denote dynamics obtained using a product-state ansatz that factorizes the vibrational degrees of freedom from the rest: ∣ψEHF(t)⟩=∣ϕ(t)⟩⊗∏ i D(λi(t), ˆbi)∣0⟩vib,i ,(B1) whereD(λ, ˆbi)≡exp [λ(ˆb† i −ˆbi)] denotes the displacement operator. In the disorder-free case (W=0) this ansatz yields an analytically t...

    work page

  3. [3]

    Truncated Wigner approximation The Truncated Wigner Approximation (TWA) [50] is a semiclassical numerical scheme that is often used to compute the quantum dynamics of many-body systems. This method is based on the phase space formalism of quantum mechanics where Hilbert space operators ˆOare mapped through the Weyl-Wigner transform to Weyl symbolsO W , fu...

    work page

  4. [4]

    Cavity (ˆax,ˆa y,ˆa z) and electronic (ˆσ x,ˆσ y,ˆσ z) degrees of freedom are treated using DTWA and are sampled with the Wigner function of a∣↑⟩or∣↓⟩state

    are treated using TWA and initially sampled with the Wigner function of the ground state of the harmonic oscillator. Cavity (ˆax,ˆa y,ˆa z) and electronic (ˆσ x,ˆσ y,ˆσ z) degrees of freedom are treated using DTWA and are sampled with the Wigner function of a∣↑⟩or∣↓⟩state

    work page

  5. [5]

    Feist, J

    J. Feist, J. Galego, and F. J. Garcia-Vidal, Polaritonic chemistry with organic molecules, ACS Photonics5, 205 (2018)

    work page 2018

  6. [6]

    Hertzog, M

    M. Hertzog, M. Wang, J. Mony, and K. B¨ orjesson, Strong light–matter interactions: A new direction within chemistry, Chemical Society Reviews48, 937 (2019)

    work page 2019

  7. [7]

    Yuen-Zhou, N

    J. Yuen-Zhou, N. C. Giebink, and R. F. Ribeiro, Polariton Chemistry: Molecules in Cavities(John Wiley & Sons, 2025)

    work page 2025

  8. [8]

    F. J. Garcia-Vidal, C. Ciuti, and T. W. Ebbesen, Manipulating matter by strong coupling to vacuum fields, Science373, eabd0336 (2021)

    work page 2021

  9. [9]

    J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Modifying chemical landscapes 13 by coupling to vacuum fields, Angewandte Chemie International Edition51, 1592 (2012)

    work page 2012

  10. [10]

    Nagarajan, A

    K. Nagarajan, A. Thomas, and T. W. Ebbesen, Chemistry under vibrational strong coupling, Journal of the American Chemical Society143, 16877 (2021)

    work page 2021

  11. [11]

    Thomas, L

    A. Thomas, L. Lethuillier-Karl, K. Nagarajan, R. M. A. Vergauwe, J. George, T. Chervy, A. Shalabney, E. Devaux, C. Genet, J. Moran, and T. W. Ebbesen, Tilting a ground-state reactivity landscape by vibrational strong coupling, Science363, 615 (2019)

    work page 2019

  12. [12]

    W. Ahn, J. F. Triana, F. Recabal, F. Herrera, and B. S. Simpkins, Modification of ground-state chemical reactivity via light–matter coherence in infrared cavities, Science380, 1165 (2023)

    work page 2023

  13. [13]

    Fregoni, F

    J. Fregoni, F. J. Garcia-Vidal, and J. Feist, Theoretical challenges in polaritonic chemistry, ACS Photonics9, 1096 (2022)

    work page 2022

  14. [14]

    Herrera and J

    F. Herrera and J. Owrutsky, Molecular polaritons for controlling chemistry with quantum optics, The Journal of Chemical Physics152, 100902 (2020)

    work page 2020

  15. [15]

    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 electrodynamics, Chemical Reviews123, 9786 (2023)

    work page 2023

  16. [16]

    Ruggenthaler, D

    M. Ruggenthaler, D. Sidler, and A. Rubio, Understanding polaritonic chemistry from ab initio quantum electrodynamics, Chemical Reviews123, 11191 (2023)

    work page 2023

  17. [17]

    Bauman, L

    N. Bauman, L. A. Cunha, A. E. I. DePrince, J. Flick, J. J. I. Foley, N. Govind, G. Groenhof, N. Hoffmann, K. Kowalski, X. Li, M. Liebenthal, N. T. Maitra, R. Manderna, M. Matouˇ sek, I. M. Mazin, D. Mejia- Rodriguez, A. Panyala, B. Peng, B. Peyton, L. Veis, N. Vu, J. D. Weidman, A. K. Wilson, R. A. Zarotiadis, and Y. Zhang, Perspective on Many-Body Method...

    work page 2025

  18. [18]

    Galego, F

    J. Galego, F. J. Garcia-Vidal, and J. Feist, Cavity- Induced Modifications of Molecular Structure in the Strong-Coupling Regime, Phys. Rev. X5, 041022 (2015)

    work page 2015

  19. [19]

    Kowalewski, K

    M. Kowalewski, K. Bennett, and S. Mukamel, Non- adiabatic dynamics of molecules in optical cavities, J. Chem. Phys.144, 10.1063/1.4941053 (2016)

    work page doi:10.1063/1.4941053 2016

  20. [20]

    R. F. Ribeiro, L. A. Mart´ ınez-Mart´ ınez, M. Du, J. Campos-Gonzalez-Angulo, and J. Yuen-Zhou, Polariton chemistry: Controlling molecular dynamics with optical cavities, Chemical Science9, 6325 (2018)

    work page 2018

  21. [21]

    H. Lang, O. Vendrell, and P. Hauke, Generalized discrete truncated wigner approximation for nonadiabatic quantum-classical dynamics, The Journal of Chemical Physics155, 024111 (2021)

    work page 2021

  22. [22]

    A. K. Kanakati, O. Vendrell, and G. Groenhof, Benchmarking mixed quantum-classical dynamics for collective electronic strong coupling (2026), arXiv:2603.05368 [physics]

    work page arXiv 2026

  23. [23]

    Sidler, C

    D. Sidler, C. Sch¨ afer, M. Ruggenthaler, and A. Rubio, Polaritonic chemistry: Collective strong coupling implies strong local modification of chemical properties, The Journal of Physical Chemistry Letters12, 508 (2021)

    work page 2021

  24. [24]

    Botzung, D

    T. Botzung, D. Hagenm¨ uller, S. Sch¨ utz, J. Dubail, G. Pupillo, and J. Schachenmayer, Dark state semilocalization of quantum emitters in a cavity, Phys. Rev. B102, 144202 (2020)

    work page 2020

  25. [25]

    Dubail, T

    J. Dubail, T. Botzung, J. Schachenmayer, G. Pupillo, and D. Hagenm¨ uller, Large random arrowhead matrices: Multifractality, semilocalization, and protected transport in disordered quantum spins coupled to a cavity, Phys. Rev. A105, 023714 (2022)

    work page 2022

  26. [26]

    Sommer, M

    C. Sommer, M. Reitz, F. Mineo, and C. Genes, Molecular polaritonics in dense mesoscopic disordered ensembles, Phys. Rev. Res.3, 033141 (2021)

    work page 2021

  27. [27]

    Wellnitz, G

    D. Wellnitz, G. Pupillo, and J. Schachenmayer, Disorder enhanced vibrational entanglement and dynamics in polaritonic chemistry, Communications Physics5, 120 (2022)

    work page 2022

  28. [28]

    J. B. P´ erez-S´ anchez, F. Mellini, N. C. Giebink, and J. Yuen-Zhou, Collective polaritonic effects on chemical dynamics suppressed by disorder, Phys. Rev. Res.6, 013222 (2024)

    work page 2024

  29. [29]

    T. Li, P. Venkatesh, Q. Shi, and A. Montoya- Castillo, For molecular polaritons, disorder and phonon timescales control the activation of dark states in the thermodynamic limit (2026), arXiv:2603.06868 [physics]

    work page arXiv 2026

  30. [30]

    J. A. ´Cwik, S. Reja, P. B. Littlewood, and J. Keeling, Polariton condensation with saturable molecules dressed by vibrational modes, Europhys. Lett.105, 47009 (2014)

    work page 2014

  31. [31]

    Herrera and F

    F. Herrera and F. C. Spano, Cavity-Controlled Chemistry in Molecular Ensembles, Physical Review Letters116, 238301 (2016)

    work page 2016

  32. [32]

    M. A. Zeb, P. G. Kirton, and J. Keeling, Exact States and Spectra of Vibrationally Dressed Polaritons, ACS Photonics5, 249 (2018)

    work page 2018

  33. [33]

    del Pino, F

    J. del Pino, F. A. Y. N. Schr¨ oder, A. W. Chin, J. Feist, and F. J. Garcia-Vidal, Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons, Physical Review Letters121, 227401 (2018)

    work page 2018

  34. [34]

    Matouˇ sek, N

    M. Matouˇ sek, N. Vu, N. Govind, J. J. I. V. Foley, and L. Veis, Polaritonic Chemistry Using the Density Matrix Renormalization Group Method, J. Chem. Theory Comput.20, 9424 (2024)

    work page 2024

  35. [35]

    Reitz, C

    M. Reitz, C. Sommer, and C. Genes, Cooperative Quantum Phenomena in Light-Matter Platforms, PRX Quantum3, 010201 (2022)

    work page 2022

  36. [36]

    Valmorra, M

    F. Valmorra, M. Br¨ oll, S. Schwaiger, N. Welzel, D. Heitmann, and S. Mendach, Strong coupling between surface plasmon polariton and laser dye rhodamine 800, Applied Physics Letters99, 051110 (2011)

    work page 2011

  37. [37]

    Christensson, B

    N. Christensson, B. Dietzek, A. Yartsev, and T. Pullerits, Electronic photon echo spectroscopy and vibrations, Vibrational Spectroscopy53, 2 (2010)

    work page 2010

  38. [38]

    Herrera and F

    F. Herrera and F. C. Spano, Theory of Nanoscale Organic Cavities: The Essential Role of Vibration- Photon Dressed States, ACS Photonics5, 65 (2018)

    work page 2018

  39. [39]

    Bhuyan, J

    R. Bhuyan, J. Mony, O. Kotov, G. W. Castellanos, J. G´ omez Rivas, T. O. Shegai, and K. B¨ orjesson, The Rise and Current Status of Polaritonic Photochemistry and Photophysics, Chemical Reviews123, 10877 (2023)

    work page 2023

  40. [40]

    M. G. Genoni, M. G. A. Paris, and K. Banaszek, Quantifying the non-gaussian character of a quantum state by quantum relative entropy, Phys. Rev. A78, 060303 (2008)

    work page 2008

  41. [41]

    Weedbrook, S

    C. Weedbrook, S. Pirandola, R. Garc´ ıa-Patr´ on, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys.84, 621 (2012)

    work page 2012

  42. [42]

    T. F. Demarie, Pedagogical introduction to the entropy of entanglement for gaussian states (2012), arXiv:1209.2748 [quant-ph]. 14

    work page arXiv 2012

  43. [43]

    S. B. Ju´ arez, Quantum Information Geometry and its classical aspect (2023), arXiv:2302.12652 [quant-ph]

    work page arXiv 2023

  44. [44]

    Eyring, The activated complex and the absolute rate of chemical reactions., Chemical Reviews17, 65 (1935)

    H. Eyring, The activated complex and the absolute rate of chemical reactions., Chemical Reviews17, 65 (1935)

    work page 1935

  45. [45]

    H. E. Avery, Dependence of rate on temperature, in Basic Reaction Kinetics and Mechanisms(Macmillan Education UK, London, 1974) pp. 47–58

    work page 1974

  46. [46]

    Groenhof, C

    G. Groenhof, C. Climent, J. Feist, D. Morozov, and J. J. Toppari, Tracking polariton relaxation with multiscale molecular dynamics simulations, The Journal of Physical Chemistry Letters10, 5476 (2019)

    work page 2019

  47. [47]

    Zhang, T

    Y. Zhang, T. Nelson, and S. Tretiak, Non-adiabatic molecular dynamics of molecules in the presence of strong light-matter interactions, The Journal of Chemical Physics151, 154109 (2019)

    work page 2019

  48. [48]

    L. J. Bond, B. Gerritsen, J. Min´ aˇ r, J. T. Young, J. Schachenmayer, and A. Safavi-Naini, Open quantum dynamics with variational non-gaussian states and the truncated wigner approximation, The Journal of Chemical Physics161, 184113 (2024)

    work page 2024

  49. [49]

    Serafini, F

    A. Serafini, F. Illuminati, and S. D. Siena, Symplectic invariants, entropic measures and correlations of gaussian states, Journal of Physics B: Atomic, Molecular and Optical Physics37, L21 (2003)

    work page 2003

  50. [50]

    Eisert, M

    J. Eisert, M. Cramer, and M. B. Plenio, Colloquium: Area laws for the entanglement entropy, Reviews of Modern Physics82, 277–306 (2010)

    work page 2010

  51. [51]

    Vidal, Efficient Simulation of One-Dimensional Quantum Many-Body Systems, Physical Review Letters 93, 040502 (2004)

    G. Vidal, Efficient Simulation of One-Dimensional Quantum Many-Body Systems, Physical Review Letters 93, 040502 (2004)

    work page 2004

  52. [52]

    Paeckel, T

    S. Paeckel, T. K¨ ohler, A. Swoboda, S. R. Manmana, U. Schollw¨ ock, and C. Hubig, Time-evolution methods for matrix-product states, Annals of Physics411, 167998 (2019)

    work page 2019

  53. [53]

    A. T. Sornborger and E. D. Stewart, Higher-order methods for simulations on quantum computers, Phys. Rev. A60, 1956 (1999)

    work page 1956

  54. [54]

    Polkovnikov, Phase space representation of quantum dynamics, Annals of Physics325, 1790 (2010)

    A. Polkovnikov, Phase space representation of quantum dynamics, Annals of Physics325, 1790 (2010)

    work page 2010

  55. [55]

    W. K. Wootters, A wigner-function formulation of finite- state quantum mechanics, Annals of Physics176, 1 (1987)

    work page 1987

  56. [56]

    Schachenmayer, A

    J. Schachenmayer, A. Pikovski, and A. M. Rey, Many-body quantum spin dynamics with monte carlo trajectories on a discrete phase space, Phys. Rev. X5, 011022 (2015)

    work page 2015

  57. [57]

    B. Zhu, A. M. Rey, and J. Schachenmayer, A generalized phase space approach for solving quantum spin dynamics, New Journal of Physics21, 082001 (2019)

    work page 2019

  58. [58]

    Yang and J

    K.-H. Yang and J. O. Hirschfelder, Generalizations of classical poisson brackets to include spin, Phys. Rev. A 22, 1814 (1980)

    work page 1980