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arxiv: 2607.06137 · v1 · pith:AOVJRIXU · submitted 2026-07-07 · hep-ph · nucl-th· quant-ph

Quantum decoherence: a study applied to quarkonium-like bound states in strongly interacting matter

Gabriele Coci , Salvatore Plumari , Giuseppe Falci This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-08 15:22 UTCglm-5.2pith:AOVJRIXUrecord.jsonopen to challenge →

classification hep-ph nucl-thquant-ph
keywords quantumdecoherenceevolutioninteractingboundcouplingmattermedium
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The pith

Expanding plasma slows quarkonium decoherence, viscosity barely matters

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

This paper models a J/psi charmonium bound state as a quantum harmonic oscillator coupled to a thermal bath representing the quark-gluon plasma, then evolves the system's density matrix under a Lindblad master equation to track how quantum coherence is lost. The central move is extending the standard static-bath Lindblad framework to include a time-dependent temperature T(t) that mimics the one-dimensional hydrodynamic expansion of the fireball produced in heavy-ion collisions. The authors find that when the bath cools as the plasma expands, decoherence proceeds more slowly than in a static bath held at the initial temperature. For LHC-like conditions (initial temperature 0.5 GeV), coherence is lost within roughly 2 fm/c, while for RHIC-like conditions (initial temperature 0.3 GeV), coherence persists beyond 5 fm/c. Viscous corrections to the expansion, modeled at eta/s = 1/4pi, produce negligible change in the decoherence timescale compared to ideal hydrodynamics. The paper also tracks the Wigner function in phase space, showing that negative fringes characteristic of quantum superposition are washed out on the same decoherence timescale, driving the system toward a classical probability distribution.

Core claim

The paper's central result is that introducing a realistic time-dependent temperature profile for the expanding QGP into the Lindblad master equation for a J/psi-like harmonic oscillator slows quantum decoherence relative to a static bath, and that this effect depends strongly on the initial temperature (RHIC vs. LHC conditions) but is insensitive to viscous corrections. The mechanism is straightforward: as the plasma expands and cools, the system-reservoir coupling strength gamma(T) decreases, so the rate at which off-diagonal density matrix elements are suppressed drops over time. At LHC temperatures the initial coupling is strong enough that coherence is destroyed in about 2 fm/c, before;

What carries the argument

Lindblad master equation in the optical regime for a damped harmonic oscillator with amplitude-coupling to a bosonic reservoir, extended to include time-dependent temperature T(t) via a multiplicative factor f(t) on the coupling coefficients. The system frequency omega_0 = 0.457 GeV is fixed from the J/psi root-mean-square radius. The dissociation rate gamma(T) is taken from phenomenological charmonium suppression calculations. Temperature evolution follows a Bjorken-like power law T(t) = T_0 * (tau_0/t)^(c_s^2), with c_s^2 = 1/3 for ideal hydrodynamics or a Boltzmann transport result for viscous expansion.

If this is right

  • If decoherence at RHIC temperatures takes longer than 5 fm/c, quarkonium states may retain partial quantum coherence through much of the fireball lifetime, meaning hadronization models that assume fully classical phase-space distributions may need revision for systems produced at lower initial temperatures.
  • The near-equivalence of ideal and viscous expansion for decoherence suggests that the dominant control parameter is the initial temperature, not the detailed hydrodynamic profile, simplifying future calculations.
  • The Wigner function evolution provides a direct bridge between the open-quantum-systems description and coalescence hadronization models, which assume Gaussian Wigner functions; the paper shows this assumption becomes valid on the decoherence timescale.
  • The framework can be extended to other quarkonium states (Upsilon, chi_c) by changing omega_0 and gamma(T), potentially yielding a hierarchy of decoherence times across the quarkonium spectrum.

Where Pith is reading between the lines

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

  • If the oscillator frequency omega_0 were allowed to vary with temperature (as it physically should, since in-medium binding energy changes), the decoherence timescales could shift substantially, particularly near T_c where color screening is strongly temperature-dependent. The paper's quantitative results are thus best read as order-of-magnitude estimates for the optical regime rather than precise
  • The observation that coherence survives beyond 5 fm/c at RHIC conditions raises the question of whether partially coherent quarkonium states could serve as quantum probes of the early-time QGP, carrying phase information from the initial production mechanism through the medium evolution.
  • The insensitivity to viscosity suggests that decoherence is controlled primarily by the integrated thermal exposure (the time-integrated coupling strength) rather than the instantaneous expansion rate, which could be tested by comparing different equations of state at fixed initial temperature.

Load-bearing premise

The oscillator frequency omega_0 representing the J/psi binding energy is held constant throughout the evolution, even as the temperature drops from 0.5 GeV to near the phase transition. In reality, the in-medium binding energy and thus the oscillator frequency should change substantially with temperature, particularly near the deconfinement transition where color screening is strongly temperature-dependent. The authors flag this themselves.

What would settle it

If allowing omega_0 to vary with temperature in a self-consistent way changed the decoherence timescale by a factor of two or more, the quantitative distinction between RHIC and LHC conditions would need to be re-established.

Figures

Figures reproduced from arXiv: 2607.06137 by Gabriele Coci, Giuseppe Falci, Salvatore Plumari.

Figure 1
Figure 1. Figure 1: FIG. 1: (color online): Population of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Time evolution of imaginary part of coherence ele [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Time evolution of the real part of coherence ele [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (color online): Time evolution of the real part of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Contour plot of Wigner distribution for initial coher [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Time evolution of Wigner function [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Time evolution of momentum distribution [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Average momentum [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (Color online) Average relative momentum [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Contour plot of initial cat state Eq. (43) with pa [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Contour plots of Wigner function [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Time evolution of ground state population of [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: (color online): Time evolution of the real part of [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: (color online): Time evolution of the imaginary part [PITH_FULL_IMAGE:figures/full_fig_p013_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Contour plots of Wigner function [PITH_FULL_IMAGE:figures/full_fig_p014_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: (color online) The real part of coherence elements [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
read the original abstract

We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of $J/\Psi$ particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.

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 / 7 minor

Summary. The manuscript studies quantum decoherence of a J/ψ-like harmonic oscillator coupled to a thermal reservoir representing the QGP, within the open quantum systems framework. The oscillator frequency ω₀ is fixed from the J/ψ RMS radius, and the dissociation rate γ(T) is taken from the TAMU model. The authors derive a Lindblad master equation in the optical regime, extend it to include a time-dependent temperature T(t) modeling 1D Bjorken expansion, and solve it numerically. The central results are: (1) in a static bath, coherence is lost on timescales of ~5 fm/c at T = 0.3 GeV; (2) with expanding medium, decoherence is slowed relative to the static case; (3) for LHC conditions (T₀ = 0.5 GeV), coherence is lost within ~2 fm/c, while for RHIC conditions (T₀ = 0.3 GeV), it persists beyond ~5 fm/c; (4) viscous corrections (η/s = 1/4π) do not significantly alter the decoherence timescale. The Wigner function evolution from cat-state initial conditions is also presented, showing classicalization and connection to coalescence hadronization models.

Significance. The paper addresses a timely question — how fast quantum coherence of quarkonium is lost in the QGP — using a well-established Lindblad framework in the optical regime. The extension to a time-dependent temperature is a natural and useful step toward realism. The model has a small number of physically motivated inputs (ω₀ from the J/ψ radius, γ(T) from an external dissociation calculation), and the decoherence timescales are genuine outputs rather than fitted parameters. The Wigner-function analysis connecting decoherence to the validity of classical coalescence hadronization is a nice conceptual contribution. The finding that viscous corrections are negligible for decoherence is a concrete, falsifiable result. The work is exploratory rather than definitive, but it provides a reasonable first estimate and a framework that can be refined.

major comments (3)
  1. Sec. VI, and Eqs. (32): The central quantitative claims (coherence lost within ~2 fm/c at LHC, persisting beyond ~5 fm/c at RHIC) depend on the decoherence rate Re(a_n) = (γ/2)·n·(1+2n̄(ω₀,T)), where n̄(ω₀,T) = 1/(e^{ω₀/T}−1). The authors fix ω₀ = 0.457 GeV (vacuum J/ψ value) throughout the evolution, even as T drops from 0.5 GeV toward T_c ≈ 0.16 GeV. In reality, the in-medium binding energy — and thus ω₀(T) — varies substantially with temperature, particularly near T_c where color screening is strongly T-dependent. Since n̄ enters the decoherence rate exponentially, a T-dependent ω₀(T) could shift the quoted timescales significantly: at early times when T₀ = 0.5 GeV, a smaller ω₀(T₀) (weaker binding) would increase n̄ and accelerate decoherence; near T_c, a larger ω₀(T_c) (stronger binding restored) would suppress n̄ exponentially and extend decoherence well beyond ~5 fm/c. The authors
  2. Sec. II.A, Eq. (17): The optical regime requires τ_S ≪ τ_R, i.e., ω₀ ≫ γ(T). With ω₀ = 0.457 GeV, this translates to γ(T) ≪ 0.457 GeV. The authors should verify and state explicitly that this condition is satisfied for the γ(T) values used at all temperatures considered (T = 0.2–0.5 GeV), particularly at the highest T where γ(T) is largest. If γ(T) approaches ω₀ at any point, the rotating-wave approximation underlying Eq. (14) breaks down, and the quantitative results in that regime would be unreliable. A figure or table of γ(T)/ω₀ versus T would address this.
  3. Sec. II.B, Eq. (22)–(23): The quasi-static approximation T(t') ≈ T(t) requires that the bath correlation time τ_E be much shorter than the hydrodynamic timescale τ_hydro. The authors state this hierarchy but do not provide estimates of τ_E. For the optical regime, τ_E ~ 1/T, which at T = 0.3 GeV gives τ_E ~ 0.66 fm, while τ_hydro ~ τ₀ = 0.6 fm — a ratio of only ~1, not a clean separation. The authors should either provide a more careful justification (e.g., estimating τ_E from the spectral density J(ω) rather than from 1/T) or acknowledge that the quasi-static approximation is marginal at the lower end of the temperature range and discuss how this affects the RHIC results in particular. This is load-bearing because the entire time-dependent T(t) framework — and hence the claim that expansion slows decoherence — rests on this approximation.
minor comments (7)
  1. Sec. II.C: The value σ_r = 0.348 fm is attributed to Table 1 of Ref. [19], but the inversion of Eq. (25) to obtain ω₀ = 0.457 GeV should show the intermediate steps (the reduced mass μ = M_c/2 = 0.7 GeV) so the reader can verify the arithmetic.
  2. Eq. (30): The approximation retaining only terms proportional to n ≫ 1 is stated to work well for n ≥ 4, with 25–40% discrepancy for n = 1,2. Since the n = 1 coherence ρ₀₁ is one of the primary observables shown in the figures, the authors should note this limitation when presenting those results.
  3. Fig. 8: The caption states that γ obtained from the exponential fit is 'equivalent to the input dissociation rate.' This is expected by construction (the Lindblad equation is built from γ), so the statement should be framed as a consistency check rather than a prediction.
  4. Sec. VI: The statement 'the bounded system, characterized by frequency ω₀ increases as the temperature decreases' is confusingly worded — ω₀ is held constant throughout. The intended meaning appears to be that the ratio ω₀/T increases. Please rephrase.
  5. Sec. V.B: The connection to coalescence hadronization (paragraph beginning 'On the one hand, Q̄Q pairs...') is interesting but speculative. A brief statement that this is a qualitative observation motivating future work, rather than an established result, would improve precision.
  6. References: Several arXiv-only citations (e.g., Refs. [35], [36], [76], [79]) should be updated to published versions if available.
  7. Typo in Sec. II.C: 'indipendent' should be 'independent' (also appears in Sec. II.A, Eq. (2) description). Similarly, 'reab-sorbed' in Sec. II.B should be 'reabsorbed,' and 'parametrization' is used inconsistently with 'parametrization' elsewhere.

Simulated Author's Rebuttal

3 responses · 2 unresolved

We thank the referee for a careful and constructive report. The comments identify three important physical issues — the temperature dependence of the binding frequency, the validity of the optical regime, and the quasi-static approximation — that we agree must be addressed more explicitly in the manuscript. Below we respond to each point. We find that two of the three require revision (one partial, one full), and for the third we provide the requested quantitative verification, which also necessitates a revision to make the check explicit in the text.

read point-by-point responses

  1. Referee: Major Comment 1 (Sec. VI, Eqs. 32): The central quantitative claims depend on fixing omega_0 = 0.457 GeV (vacuum J/psi value) throughout the evolution, even as T drops from 0.5 GeV toward T_c. In reality, the in-medium binding energy — and thus omega_0(T) — varies substantially with temperature, particularly near T_c where color screening is strongly T-dependent. Since n_bar enters the decoherence rate exponentially, a T-dependent omega_0(T) could shift the quoted timescales significantly.

    Authors: The referee is correct that a temperature-dependent omega_0(T) could quantitatively shift the decoherence timescales, and we agree this limitation must be stated more prominently. In the current manuscript, we acknowledge on p. 13 that 'this difference depends strongly on the way the dissociation coefficient gamma(T) varies with temperature, as well as on our assumption that the frequency omega_0 remains unaffected by the environment,' and we list the introduction of a T-dependent omega_0 as a future direction in the Conclusions. However, we agree this is insufficiently emphasized given its quantitative impact. We will revise the manuscript to include a dedicated discussion of this point in Sec. VI, explicitly noting the direction of the bias the referee identifies: at early times (high T), a smaller in-medium omega_0 would increase n_bar and accelerate decoherence, while near T_c, a larger omega_0 would suppress n_bar exponentially and extend decoherence. We will also add a quantitative estimate of the sensitivity. That said, we note that a fully self-consistent omega_0(T) is not straightforward to implement within the current framework: the Lindblad equation in the optical regime requires omega_0 to define the system Hamiltonian and the Fock basis at all times, and introducing a time-dependent omega_0(t) would require re-deriving the master equation with a time-dependent system frequency, which involves additional non-trivial terms (parametric driving) beyond the current amplitude-coupling Lindblad form. This is a genuine technical limitation of the present framework, not merely a parameter choice. We will therefore implement a partial revision: adding the sensitivity discussion and the caveat, while deferring the full T-dependent omega_0 treatment to a future study,, revision: partial

  2. Referee: Major Comment 2 (Sec. II.A, Eq. 17): The optical regime requires tau_S << tau_R, i.e., omega_0 >> gamma(T). With omega_0 = 0.457 GeV, this translates to gamma(T) << 0.457 GeV. The authors should verify and state explicitly that this condition is satisfied for the gamma(T) values used at all temperatures considered (T = 0.2-0.5 GeV), particularly at the highest T where gamma(T) is largest. A figure or table of gamma(T)/omega_0 versus T would address this.

    Authors: We agree that this verification should be explicit in the manuscript. We have checked the condition gamma(T) << omega_0 for the TAMU model dissociation rates used in this work (from Grandchamp and Rapp, Refs. [18, 58]). At T = 0.5 GeV (the highest temperature considered), the dissociation rate gamma is approximately 0.08-0.1 GeV, giving gamma/omega_0 ~ 0.2. At T = 0.4 GeV, gamma/omega_0 ~ 0.1, and at T = 0.2 GeV the ratio is well below 0.05. The condition gamma(T) << omega_0 is thus satisfied throughout the temperature range, though we acknowledge the ratio is largest at the highest temperatures and the separation is not as dramatic as in typical quantum optics applications. We will add a table or figure of gamma(T)/omega_0 versus T in the revised manuscript, along with an explicit statement that the optical regime condition is satisfied at all temperatures studied, while noting that the margin is narrowest at T ~ 0.5 GeV and results at the highest temperatures should be interpreted with this caveat. We thank the referee for this concrete and actionable suggestion. revision: yes

  3. Referee: Major Comment 3 (Sec. II.B, Eqs. 22-23): The quasi-static approximation T(t') ~ T(t) requires that the bath correlation time tau_E be much shorter than the hydrodynamic timescale tau_hydro. The authors state this hierarchy but do not provide estimates of tau_E. For the optical regime, tau_E ~ 1/T, which at T = 0.3 GeV gives tau_E ~ 0.66 fm, while tau_hydro ~ tau_0 = 0.6 fm — a ratio of only ~1, not a clean separation. The authors should either provide a more careful justification or acknowledge that the quasi-static approximation is marginal at the lower end of the temperature range and discuss how this affects the RHIC results in particular.

    Authors: The referee raises a legitimate concern that we cannot fully resolve within the present framework. The estimate tau_E ~ 1/T is a reasonable order-of-magnitude proxy for the bath correlation time, and at T = 0.3 GeV it indeed gives tau_E ~ 0.66 fm, comparable to tau_hydro = tau_0 = 0.6 fm. A more rigorous estimate would require computing tau_E from the spectral density J(omega) of the reservoir, which in our model is not independently specified — it enters only through the dissociation rate gamma = 2*pi*J(omega_0). Without an explicit form of J(omega) over a range of frequencies, we cannot extract a model-independent tau_E. We therefore agree that the quasi-static approximation is marginal at the lower end of the temperature range, and this directly affects the RHIC results (T_0 = 0.3 GeV), which are precisely the cases where coherence is claimed to persist beyond ~5 fm/c. We will revise the manuscript to: (1) include the explicit estimate tau_E ~ 1/T and the resulting ratio tau_E/tau_hydro at representative temperatures; (2) acknowledge that the separation is marginal at T ~ 0.3 GeV and improves at higher T; (3) add a caveat that the RHIC results, in particular, should be interpreted with this limitation in mind. We note that at LHC temperatures (T_0 = 0.5 GeV), tau_E ~ 0.4 fm and the ratio tau_E/tau_hydro ~ 0.67 is somewhat better, though still not a clean hierarchy. This is a genuine standing limitation of the quasi-static approach that we will be transparent about rather than attempting to dismiss. revision: yes

standing simulated objections not resolved
  • The quasi-static approximation (Major Comment 3) is genuinely marginal at the lower end of the temperature range (T ~ 0.3 GeV), and we cannot provide a more rigorous justification without an explicit spectral density J(omega) beyond the single point J(omega_0). The RHIC results are the most affected, and we can only flag this caveat rather than resolve it.
  • A fully self-consistent treatment of omega_0(T) (Major Comment 1) requires re-deriving the Lindblad master equation with a time-dependent system frequency, which goes beyond the current amplitude-coupling framework. We can discuss the sensitivity but cannot implement the full treatment in this manuscript.

Circularity Check

0 steps flagged

No significant circularity: decoherence timescales are genuine outputs of the Lindblad evolution with externally-provided inputs

full rationale

The paper's derivation chain is self-contained against external benchmarks. The two key input parameters are: (1) ω₀ = 0.457 GeV, fixed from the J/ψ RMS radius (PDG data, Ref. [52]) via Eq. (25), and (2) γ(T), the dissociation rate taken from the TAMU model (Refs. [1, 18] — external to the present authors). The Lindblad master equation (Eq. 14) is a standard textbook derivation in the optical regime (Born-Markov approximation, amplitude coupling). The central quantitative results — coherence lost within ~2 fm/c at LHC conditions and persisting beyond ~5 fm/c at RHIC conditions — are outputs of numerically solving the Lindblad equation with a time-dependent T(t) from Bjorken hydrodynamics (Eq. 44). These timescales are not fitted to data; they emerge from the evolution. The analytic decoherence rate Re(a_n) = (γ/2)n(1+2n̄) in Eq. (32) is derived as a large-n approximation of Eq. (18), not a fit. Figure 8, where the fitted momentum damping rate recovers the input γ, is explicitly framed by the authors as a consistency check of the Fokker-Planck correspondence ('we find to be equivalent to the input dissociation rate from the TAMU model'), not as a prediction. The viscous correction comparison uses an external Boltzmann transport code (Ref. [74], co-authored by S. Plumari) to generate the T(t) profile with η/s = 1/4π; this is a supporting input for one comparison case, not the central derivation. The self-citations to the Catania group's transport code and coalescence work (Refs [69-71, 73-79]) are not load-bearing for the decoherence results — they provide the viscous T(t) profile for a secondary comparison and context for future hadronization studies. No step in the derivation of the decoherence timescales reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The paper does not invent new particles, forces, or entities. It uses a harmonic oscillator as a proxy for J/psi, which is a modeling simplification rather than an invented entity. All parameters are either physical inputs (masses, temperatures) or taken from external models (TAMU dissociation rates). The quasi-static Markov approximation is the main ad hoc element.

free parameters (6)
  • omega_0 (system frequency) = 0.457 GeV
    Fixed by matching the harmonic oscillator ground-state width to the J/psi RMS radius (sigma_r = 0.348 fm from Ref. [19]). Not fitted to decoherence data, but a model input chosen to represent the physical system.
  • gamma(T) (dissociation rate) = Temperature-dependent, from TAMU model [18]
    Phenomenologically inferred from quarkonium in-medium dissociation widths calculated from a non-perturbative many-body theory. Used as the Lindblad dissipation coefficient. Not fitted to the paper's own results.
  • alpha (coherent/cat state parameter) = 1 or 2
    Initial condition parameter for the density matrix, chosen to illustrate decoherence dynamics. Not a physical parameter fitted to data.
  • T_0 (initial temperature) = 0.3-0.5 GeV
    Physical input representing RHIC vs. LHC initial conditions, not a fitted parameter.
  • tau_0 (initial proper time) = 0.6 fm
    Set from Bjorken hydrodynamics convention. Standard physical input.
  • c_s^2 (speed of sound squared) = 1/3 (ideal) or from Boltzmann (viscous)
    Controls the cooling law T(t) = T_0 (tau_0/t)^(c_s^2). Standard hydrodynamic input.
axioms (5)
  • domain assumption Born-Markov approximation: the total density matrix factorizes as rho_t ~ rho(t) x rho_R and bath correlations decay fast (tau_E << tau_R).
    Standard OQS assumption invoked in Sec. II.A (Eq. 6) to derive the Lindblad master equation. Validity depends on the coupling strength and bath properties.
  • domain assumption Optical regime hierarchy: tau_S << tau_R, meaning the system frequency omega_0 >> damping rate gamma. Justified by E_B ~ omega_0 >= T for J/psi.
    Invoked in Sec. II.A (Eq. 17) to justify the rotating-wave approximation. The paper checks that E_B ~ omega_0 = 0.457 GeV >= T for the temperatures considered (0.2-0.5 GeV), but at T=0.5 GeV this is marginal.
  • ad hoc to paper Quasi-static approximation for time-dependent T(t): T(t') ~ T(t) during the bath correlation time, justified by tau_E << tau_hydro.
    Invoked in Sec. II.B (Eq. 22-23) to extend the Markov master equation to time-dependent temperature. The condition tau_E << tau_hydro is stated but not quantitatively verified for the QGP parameters used.
  • ad hoc to paper The system frequency omega_0 remains constant and unaffected by the environment throughout the evolution.
    Stated in Sec. VI: 'our assumption that the frequency omega_0 remains unaffected by the environment.' This ignores in-medium modifications of the binding energy, which are known to be significant near Tc.
  • domain assumption The QGP can be modeled as a static or 1D-expanding thermal bath of independent bosonic oscillators with amplitude coupling to the quarkonium.
    The reservoir model (Eq. 2-3) is a standard spin-boson type model. Its applicability to QGP degrees of freedom is a modeling assumption, not derived from QCD.

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