pith. sign in

arxiv: 2605.23322 · v1 · pith:LYDIDESMnew · submitted 2026-05-22 · 🪐 quant-ph · cond-mat.other

Quantum viscosity mechanism of the dissipative dynamics in the Dicke model expressed via Lindblad equation of motion

M.E.S.Beck , S.S.Seidov , S.I.Muhkin This is my paper

Pith reviewed 2026-05-25 04:34 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.other
keywords Dicke modelsuperradiant phaseLindblad equationquantum viscositythermal bathzero temperaturevirtual excitationspolaritonic condensate
0
0 comments X

The pith

Effective viscosity in the superradiant Dicke model survives at zero temperature from virtual excitations in the thermal bath.

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

The paper derives the Lindblad equation for the extended Dicke model in the superradiant phase coupled to a Caldeira-Leggett bath. The resulting semiclassical equations for the polaritonic condensate contain a viscosity term whose nonzero contribution at T approaching zero carries the prefactor nB(ω, T) + 1. This term indicates that virtual excitations of bath oscillators produce the dissipation. The Lindbladian is shown to require condensate-shifted photon operators and Holstein-Primakoff pseudospin operators so the system relaxes to its minimum-energy state at zero temperature.

Core claim

In the superradiant phase of the Extended Dicke model, derivation of the Lindblad equation from coupling to a thermal bath shows that effective viscosity in the semiclassical polariton dynamics survives the T -> 0 limit. The surviving term arises from the factor nB(ω, T) + 1, demonstrating that virtual excitations of harmonic oscillators in the bath generate this viscosity. Correct construction of the Lindbladian uses condensate-shifted creation and annihilation operators for photons together with Holstein-Primakoff operators for the two-level systems, ensuring relaxation to the ground state at zero temperature.

What carries the argument

Lindblad superoperator built from condensate-shifted photon operators and Holstein-Primakoff pseudospin operators, producing a viscosity contribution proportional to nB(ω, T) + 1.

If this is right

  • The polaritonic condensate experiences damping that does not disappear at absolute zero.
  • The damping originates in virtual excitations of the bath rather than real thermal population.
  • Semiclassical motion equations for the condensate include this temperature-independent viscosity term.
  • Only the shifted-operator Lindbladian allows the system to reach its true ground state at T = 0.

Where Pith is reading between the lines

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

  • Similar virtual-excitation mechanisms may produce residual dissipation in other collective-excitation models at low temperature.
  • The result suggests that zero-temperature open-system dynamics in cavity QED can be tested by measuring damping rates in atomic or circuit realizations of the Dicke model.
  • The operator-shift requirement may generalize to other phases or driven-dissipative systems where ground-state relaxation must be enforced.

Load-bearing premise

The Lindbladian must be constructed with condensate-shifted photon operators and Holstein-Primakoff pseudospins to make the system relax to its minimum energy state at zero temperature.

What would settle it

Explicit computation of the Lindblad equation with the shifted operators that yields a viscosity coefficient vanishing as T -> 0, or measurement of zero damping rate for the polaritonic condensate at sufficiently low temperature in a Dicke-model realization.

Figures

Figures reproduced from arXiv: 2605.23322 by M.E.S.Beck, S.I.Muhkin, S.S.Seidov.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic depiction of the rotated and shifted mini [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The semi-classical dynamics of the energy and spin [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The semi-classical dynamics of the energy and super [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Quantum dissipation is studied in the superradiant phase of the Extended Dicke model. It is demonstrated analytically by quantum mechanical derivation of the Lindblad equation for the Dicke model in the superradiant state coupled to Caldeira-Leggett thermal bath, that the effective viscosity appearing in the semiclassical equations of motion of polaritonic condensate survives in the zero temperature limit T -> 0. The nonzero contribution to viscosity contains prefactor nB ({\omega}, T ) + 1 with the Bose-Einstein function nB of harmonic oscillators in the thermal bath, indicating that virtual excitations of harmonic oscillators in the thermal bath coupled to the polaritons of Dicke model give rise to effective viscosity in the T -> 0 limit. Besides, it is demonstrated analytically, that correct expression for Lindbladian in the superradiant phase should be built using condensate-shifted creation and annihilation operators of the photons and pseudospin operators in Holstein-Primakoff representation of the coupled to photons two-level systems in order the system could relax to its minimum energy in T -> 0 limit due to thermal bath provided effective viscosity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims an analytical derivation of the Lindblad master equation for the Extended Dicke model in the superradiant phase coupled to a Caldeira-Leggett bath. It asserts that the effective viscosity in the semiclassical polariton equations of motion survives at T=0 with a nonzero contribution proportional to n_B(ω, T) + 1 arising from virtual excitations of bath oscillators, and that the correct Lindbladian requires condensate-shifted photon operators together with Holstein-Primakoff pseudospin operators to ensure relaxation to the minimum-energy state at T=0.

Significance. If the derivation and operator mappings are correct, the result would clarify the microscopic origin of quantum friction in superradiant cavity QED systems and show how virtual bath processes can produce dissipation even at zero temperature. The parameter-free character of the viscosity term (if truly obtained without additional assumptions) would strengthen the claim.

major comments (2)
  1. [Abstract / main derivation (no numbered equations supplied)] The central claim that the Lindblad dissipator, after condensate shift and Holstein-Primakoff replacement, yields a semiclassical viscous term whose T→0 limit is nonzero and proportional to the +1 part of n_B(ω, T) + 1 is asserted but supported by no explicit intermediate steps or equations mapping the microscopic system-bath interaction to the jump operators and rates. Without these steps the survival of the viscosity term cannot be verified.
  2. [Abstract / Lindblad construction paragraph] The requirement that the Lindbladian must be constructed with shifted photon operators and Holstein-Primakoff pseudospins in order for the system to relax to its minimum energy at T=0 is stated without a comparative calculation showing why alternative operator choices produce incorrect steady states or fail to generate the claimed rates.
minor comments (2)
  1. The title refers to the 'Dicke model' while the abstract refers to the 'Extended Dicke model'; the precise Hamiltonian (including any additional terms) should be stated explicitly at the outset.
  2. The Bose-Einstein function n_B(ω, T) is introduced without an equation defining its argument or the frequency ω that enters the viscosity prefactor.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight areas where the presentation of the derivation can be strengthened. We agree that additional explicit steps and comparisons will improve clarity and will incorporate them in a revised manuscript.

read point-by-point responses

  1. Referee: The central claim that the Lindblad dissipator, after condensate shift and Holstein-Primakoff replacement, yields a semiclassical viscous term whose T→0 limit is nonzero and proportional to the +1 part of n_B(ω, T) + 1 is asserted but supported by no explicit intermediate steps or equations mapping the microscopic system-bath interaction to the jump operators and rates. Without these steps the survival of the viscosity term cannot be verified.

    Authors: We agree that the manuscript would benefit from displaying the intermediate algebraic steps. The derivation proceeds by first displacing the photon operators by the condensate amplitude, applying the Holstein-Primakoff transformation to the collective spin operators around the mean-field minimum, inserting the resulting system-bath coupling into the standard Born-Markov master equation, and identifying the jump operators as the shifted lowering operators. The ensuing rates retain the factor (n_B(ω,T) + 1) from the bath correlation functions, which remains finite at T=0. A new subsection will be added that walks through these mappings with numbered equations. revision: yes

  2. Referee: The requirement that the Lindbladian must be constructed with shifted photon operators and Holstein-Primakoff pseudospins in order for the system to relax to its minimum energy at T=0 is stated without a comparative calculation showing why alternative operator choices produce incorrect steady states or fail to generate the claimed rates.

    Authors: The manuscript emphasizes that the unshifted operators do not respect the displaced vacuum of the superradiant phase and therefore drive relaxation toward an unphysical state. We will add a short comparative paragraph (or appendix) that contrasts the steady-state condition obtained with shifted versus unshifted operators, confirming that only the shifted form yields a vanishing effective force at the energy minimum when T→0. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation from microscopic bath model appears self-contained

full rationale

The paper claims an analytical derivation of the Lindblad equation starting from the Caldeira-Leggett bath Hamiltonian, followed by a change to condensate-shifted photon operators and Holstein-Primakoff pseudospins, yielding the nB(ω,T)+1 viscosity term that survives at T=0. No quoted step reduces the target result to a fitted parameter, a self-citation chain, or a definition that presupposes the viscosity outcome. The operator choice is presented as required for T=0 relaxation, but this is justified within the derivation rather than imported by fiat or prior self-work. The central claim therefore retains independent content from the microscopic starting point and does not collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the Caldeira-Leggett bath model, the Holstein-Primakoff approximation in the superradiant phase, and the requirement that the Lindbladian be written with condensate-shifted operators; none of these are independently verified in the abstract.

axioms (2)
  • domain assumption Caldeira-Leggett thermal bath coupling produces the claimed virtual-excitation contribution to viscosity at T=0
    Invoked in the derivation of the Lindblad equation for the superradiant state
  • domain assumption Holstein-Primakoff representation plus condensate shift yields the correct minimum-energy relaxation
    Stated as necessary for the system to relax properly at T=0

pith-pipeline@v0.9.0 · 5745 in / 1450 out tokens · 19932 ms · 2026-05-25T04:34:32.514462+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

  1. [1]

    Physical Review , volume=

    Coherence in spontaneous radiation processes , author=. Physical Review , volume=. 1954 , publisher=

    work page 1954

  2. [2]

    Annals of Physics , volume=

    On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model , author=. Annals of Physics , volume=. 1973 , publisher=

    work page 1973

  3. [3]

    Communications in Mathematical Physics , volume=

    On the generators of quantum dynamical semigroups , author=. Communications in Mathematical Physics , volume=. 1976 , publisher=

    work page 1976

  4. [4]

    Journal of Mathematical Physics , volume=

    Completely positive dynamical semigroups of N-level systems , author=. Journal of Mathematical Physics , volume=. 1976 , publisher=

    work page 1976

  5. [5]

    1991 , journal =

    An open systems approach to quantum optics , author =. 1991 , journal =

    work page 1991

  6. [6]

    2007 , journal=

    The Theory of Open Quantum Systems , author =. 2007 , journal=

    work page 2007

  7. [7]

    Physical Review Letters , volume=

    Influence of dissipation on quantum tunneling in macroscopic systems , author=. Physical Review Letters , volume=. 1981 , publisher=

    work page 1981

  8. [8]

    Physical Review A , volume=

    Cavity quantum electrodynamics in the nonperturbative regime , author=. Physical Review A , volume=. 2018 , publisher=

    work page 2018

  9. [9]

    Physical Review A , volume=

    Ultrastrong-coupling phenomena beyond the Dicke model , author=. Physical Review A , volume=. 2016 , publisher=

    work page 2016

  10. [10]

    Physical Review A , volume=

    Breakdown of gauge invariance in ultrastrong-coupling cavity QED , author=. Physical Review A , volume=. 2018 , publisher=

    work page 2018

  11. [11]

    Physical Review A , volume=

    Relaxation breakdown and resonant tunneling in ultrastrong-coupling cavity QED , author=. Physical Review A , volume=. 2023 , publisher=

    work page 2023

  12. [12]

    Journal of Physics A: Mathematical and Theoretical , volume=

    Spontaneous symmetry breaking and Husimi Q-functions in extended Dicke model , author=. Journal of Physics A: Mathematical and Theoretical , volume=. 2020 , publisher=

    work page 2020

  13. [13]

    Physical Review A , volume=

    First-order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction , author=. Physical Review A , volume=. 2018 , publisher=

    work page 2018

  14. [14]

    Bound luminosity

    “Bound luminosity” state in the extended Dicke model , author=. Annals of Physics , volume=. 2023 , publisher=

    work page 2023

  15. [15]

    Physical Review A , volume=

    Quantum Dicke battery supercharging in the bound-luminosity state , author=. Physical Review A , volume=. 2024 , publisher=

    work page 2024

  16. [16]

    The European Physical Journal B , volume=

    Quantum thermal machines and batteries , author=. The European Physical Journal B , volume=. 2021 , publisher=

    work page 2021

  17. [17]

    Physical Review E—Statistical, Nonlinear, and Soft Matter Physics , volume=

    Entanglement boost for extractable work from ensembles of quantum batteries , author=. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics , volume=. 2013 , publisher=

    work page 2013

  18. [18]

    Physical Review A , volume=

    Quantum fluctuations and correlations in open quantum Dicke models , author=. Physical Review A , volume=. 2022 , publisher=

    work page 2022

  19. [19]

    Physical Review Letters , volume=

    Suppressing and restoring the dicke superradiance transition by dephasing and decay , author=. Physical Review Letters , volume=. 2017 , publisher=

    work page 2017

  20. [20]

    Physical Review A , volume=

    Superconducting transmon qubit-resonator quantum battery , author=. Physical Review A , volume=. 2023 , publisher=

    work page 2023

  21. [21]

    Physical Review B , volume=

    Ultrafast charging in a two-photon Dicke quantum battery , author=. Physical Review B , volume=. 2020 , publisher=

    work page 2020

  22. [22]

    Mathematische Annalen , volume=

    Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt , author=. Mathematische Annalen , volume=. 1895 , publisher=

    work page

  23. [23]

    2005 , publisher=

    Applications of the Theory of Matrices , author=. 2005 , publisher=

    work page 2005

  24. [24]

    Aip Advances , volume=

    A short introduction to the Lindblad master equation , author=. Aip Advances , volume=. 2020 , publisher=

    work page 2020

  25. [25]

    Concepts of Many-Body Physics , author =

    work page

  26. [26]

    NITheP Mini School Introduction to Open Quantum Systems , author =

    work page

  27. [27]

    1972 , publisher=

    Handbook of Mathematical Functions , author=. 1972 , publisher=

    work page 1972

  28. [28]

    arXiv preprint arXiv:1908.01187 , year=

    Lindblad dynamics of the damped and forced quantum harmonic oscillator , author=. arXiv preprint arXiv:1908.01187 , year=

    work page arXiv 1908

  29. [29]

    Physical Review A , volume=

    Dissipation and ultrastrong coupling in circuit QED , author=. Physical Review A , volume=. 2011 , publisher=

    work page 2011

  30. [30]

    Physical Review A , volume=

    Dissipation and themral noise in hybrid quantum system in the ultrastrong-coupling regime , author=. Physical Review A , volume=. 2018 , publisher=

    work page 2018

  31. [31]

    Batteries , volume=

    Off-resonant Dicke Quantum Battery: Charging by Vitual Photons , author=. Batteries , volume=. 2023 , publisher=

    work page 2023

  32. [32]

    IEEE Transactions on Quantum Engineering , volume=

    Preparing Dicke states on a quantum computer , author=. IEEE Transactions on Quantum Engineering , volume=. 2020 , publisher=

    work page 2020

  33. [33]

    bound luminosity

    Dicke model semiclassical dynamics in superradiant dipolar phase in the “bound luminosity” state , author=. Journal of Experimental and Theoretical Physics , volume=. 2021 , publisher=

    work page 2021

  34. [34]

    Physical Review A , volume=

    Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top , author=. Physical Review A , volume=. 2023 , publisher=

    work page 2023

  35. [35]

    Physical Review Letters , volume =

    Photon Condensation and Enhanced Magnetism in Cavity QED , author =. Physical Review Letters , volume =. 2021 , month =. doi:10.1103/PhysRevLett.127.167201 , url =

    work page doi:10.1103/physrevlett.127.167201 2021

  36. [36]

    Nature Reviews Physics , volume=

    Ultrastrong coupling between light and matter , author=. Nature Reviews Physics , volume=. 2019 , publisher=

    work page 2019

  37. [37]

    Physical Review Letters , volume=

    Photon blockade in the ultrastrong coupling regime , author=. Physical Review Letters , volume=. 2012 , publisher=

    work page 2012

  38. [38]

    Results in Physics , volume=

    Finite-temperature Dicke phase transition and the collapse of superradiant phase in an optomechanical-atomic cavity , author=. Results in Physics , volume=. 2021 , publisher=

    work page 2021

  39. [39]

    arXiv preprint arXiv:2410.00966 , year=

    Mumax3-cQED: an extension of Mumax3 to simulate magnon-photon interactions in cavity QED , author=. arXiv preprint arXiv:2410.00966 , year=

    work page arXiv

  40. [40]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter collaboration edition editor eid eprint howpublished institution isbn journal key month note number numpages organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.co...

    work page

  41. [41]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

    work page