arxiv: 2604.07982 · v1 · submitted 2026-04-09 · ✦ hep-ph · hep-th· nucl-th

Recognition: unknown

Memory effect on the heavy quark dynamics in hot QCD matter

Jai Prakash, Ling Hai Li, Yifeng Sun, Ying Shan Zhao

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:36 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th

keywords heavy quarksquark-gluon plasmamemory effectsgeneralized Langevin equationfractional derivativesthermal noiseheavy-ion collisionsQCD matter

0 comments

The pith

Time-correlated thermal noise with memory substantially alters heavy quark dynamics in the quark-gluon plasma.

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

The paper investigates heavy quark motion through hot quark-gluon plasma when thermal fluctuations carry memory, meaning the noise at one time remains correlated with earlier times. It replaces the usual random force in the Langevin equation with power-law correlated noise generated by a Caputo fractional derivative whose order sets the memory strength. The authors compute the resulting momentum autocorrelation, the growth of average squared momentum and displacement, the average kinetic energy, and the higher central moments of the transverse-momentum distribution. A sympathetic reader cares because heavy quarks serve as probes of the plasma created in heavy-ion collisions, and any systematic change in their trajectories affects how experimenters extract plasma properties from observed particle spectra.

Core claim

Incorporating memory through time-correlated thermal noise with power-law decay in the generalized Langevin equation produces clear deviations from the memoryless case: the momentum correlation function decays more slowly, the average squared momentum and displacement evolve differently, the kinetic energy acquires a distinct time dependence, and the normalized central moments of the heavy-quark transverse-momentum distribution depart from Gaussian values. These modifications are controlled by the fractional order parameter that tunes the strength of the memory.

What carries the argument

A generalized Langevin equation whose driving noise is generated by the Caputo fractional derivative of order nu, yielding power-law time correlations whose strength is set by nu.

If this is right

The average squared momentum of heavy quarks grows more slowly at intermediate times than in the standard Brownian model.
The mean squared displacement acquires a sub-diffusive or super-diffusive regime depending on the memory parameter.
Higher central moments of the transverse-momentum distribution become non-Gaussian, altering the shape of spectra measured in experiments.
The memory-induced changes remain visible even after the heavy quark has traversed several femtometers of plasma.

Where Pith is reading between the lines

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

If the memory description holds, transport coefficients extracted from heavy-quark data under the assumption of white noise would need systematic correction.
The same fractional-noise framework could be applied to other probes such as jets or light quarks to test whether non-Markovian effects appear more broadly in the plasma.
Re-analysis of existing LHC or RHIC heavy-flavor data with varying memory strength might reveal preferred values of the fractional order that improve agreement with measured flow and suppression patterns.

Load-bearing premise

The thermal fluctuations experienced by heavy quarks inside the quark-gluon plasma can be faithfully represented by power-law correlated noise coming from a Caputo fractional derivative whose order is a free parameter.

What would settle it

A lattice calculation or direct experimental extraction of the heavy-quark momentum autocorrelation function that shows purely exponential decay with no power-law tail at late times would falsify the claim that memory effects substantially change the dynamics.

Figures

Figures reproduced from arXiv: 2604.07982 by Jai Prakash, Ling Hai Li, Yifeng Sun, Ying Shan Zhao.

**Figure 1.** Figure 1: presents a comparison between the analytical results (solid lines) given by Eq. (42) and the corresponding numerical results (dashed lines) obtained from Eq. (30) with γ = 0, for the time evolution of ⟨p 2 (t)⟩ at several values of the memory parameter ν. The black solid line, corresponding to 2Dt, represents the Markovian limit of pure diffusion driven by white noise in the absence of memory. For very … view at source ↗

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: KE versus time of the HQs, considering the con [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

read the original abstract

We study the heavy quark dynamics in the presence of memory within the framework of a generalized Langevin equation. Time correlated thermal noise with power-law decay is generated by a fractional differential equation, formulated using the Caputo fractional derivative with order parameter $\nu$. The effect of memory is calculated through the momentum correlation, the time evolution of the average squared momentum, the average squared displacement, and the average kinetic energy. The effect of memory is further studied for the higher normalised central moments of the heavy quark transverse-momentum distribution. The results indicate that time correlated thermal noise substantially influences heavy quark dynamics in the quark gluon plasma.

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.

Desk Editor's Note private letter to a colleague

The paper replaces white noise in the heavy-quark Langevin equation with power-law correlated noise via a Caputo fractional derivative of order nu, then shows changes in momentum correlations and higher pT moments, but nu remains an unconstrained free parameter.

read the letter

The core move is to take the standard Langevin description of heavy quarks in hot QCD matter and swap the usual delta-correlated thermal noise for noise with power-law memory, generated through the Caputo fractional derivative of order nu. They then track how this changes the momentum autocorrelation, the growth of , the mean squared displacement, the average kinetic energy, and the higher normalized central moments of the transverse-momentum distribution. That last part on the moments is a modest but concrete extension beyond the usual drag and diffusion focus in the literature. The calculations themselves look direct once the fractional operator is in place, and the qualitative differences from the white-noise case are reported for several values of nu. That gives a clear picture of parametric sensitivity inside the model. The main limitation is that nu is introduced purely as a knob for memory strength with no independent QCD calculation or matching to gluon correlators or lattice data to fix it. The reported influence on the dynamics therefore tracks the choice of nu rather than emerging as a robust prediction from the medium. The abstract states that the correlated noise substantially affects the observables, yet supplies no numerical values, uncertainties, or direct comparisons that would let a reader judge the size of the effect against real data or other models. Without that anchoring, the work stays at the level of an exploratory variation rather than a constrained result. This is the sort of incremental modeling paper that specialists in heavy-quark transport might want to see for the fractional-derivative technique and the moment analysis. It is coherent on its own terms and shows clear engagement with the existing Langevin framework, so it is worth sending to referees even if the central claim needs more grounding in the review process.

Referee Report

2 major / 1 minor

Summary. The paper studies heavy quark dynamics in hot QCD matter via a generalized Langevin equation that incorporates memory through time-correlated thermal noise with power-law decay, generated using a Caputo fractional derivative of order ν. It computes the impact on momentum correlations, time evolution of <p²(t)>, mean squared displacement, average kinetic energy, and higher normalized central moments of the transverse momentum distribution, concluding that such correlated noise substantially influences the dynamics relative to the standard white-noise case.

Significance. If ν could be fixed by an independent QCD calculation (e.g., matching the noise autocorrelation to the gluon correlator), the approach would usefully explore non-Markovian transport effects relevant to heavy-flavor observables in heavy-ion collisions. The inclusion of higher moments is a constructive step toward connecting to experimental p_T distributions. As formulated, however, the work mainly demonstrates sensitivity to an unconstrained parameter rather than a QCD-derived physical effect.

major comments (2)

[Model formulation (Caputo derivative definition)] The order parameter ν is introduced as a free parameter that 'represents memory strength' (abstract and model section) without an independent derivation from QCD, such as matching to the frequency-dependent heavy-quark self-energy or lattice gluon-field correlators. Consequently, all reported differences in <p²(t)>, displacement, and moments are functions of this choice and do not constitute an emergent prediction of memory effects inside hot QCD matter.
[Results and conclusions] The central claim that 'time correlated thermal noise substantially influences heavy quark dynamics' (abstract) rests on qualitative statements; the manuscript supplies no quantitative results, error estimates, or direct comparison to lattice QCD heavy-quark diffusion coefficients or experimental heavy-flavor data, preventing assessment of whether the changes survive for any physically motivated range of ν.

minor comments (1)

[Method section] Notation for the generalized Langevin equation and the precise implementation of the Caputo fractional derivative (including boundary conditions and numerical scheme) should be stated explicitly with equation numbers for reproducibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and have made revisions to clarify the phenomenological nature of the model while strengthening the quantitative presentation of results.

read point-by-point responses

Referee: [Model formulation (Caputo derivative definition)] The order parameter ν is introduced as a free parameter that 'represents memory strength' (abstract and model section) without an independent derivation from QCD, such as matching to the frequency-dependent heavy-quark self-energy or lattice gluon-field correlators. Consequently, all reported differences in <p²(t)>, displacement, and moments are functions of this choice and do not constitute an emergent prediction of memory effects inside hot QCD matter.

Authors: We agree that ν is introduced as a phenomenological parameter to control the strength of memory in the time-correlated noise. The manuscript's goal is to explore the consequences of such non-Markovian dynamics within the generalized Langevin framework for heavy quarks in hot QCD matter, rather than to derive ν ab initio. In the revised version we have added a dedicated paragraph in the model section outlining how ν could be constrained in future work by matching the noise autocorrelation function to lattice QCD gluon correlators or the frequency-dependent heavy-quark self-energy. The present study therefore demonstrates the sensitivity of observables to memory effects once such a parameter is allowed, which we view as a necessary first step before a fully QCD-derived implementation. revision: partial
Referee: [Results and conclusions] The central claim that 'time correlated thermal noise substantially influences heavy quark dynamics' (abstract) rests on qualitative statements; the manuscript supplies no quantitative results, error estimates, or direct comparison to lattice QCD heavy-quark diffusion coefficients or experimental heavy-flavor data, preventing assessment of whether the changes survive for any physically motivated range of ν.

Authors: We have expanded the results section with explicit quantitative comparisons: relative deviations (in percent) of <p²(t)>, mean-squared displacement, average kinetic energy, and the normalized central moments are now tabulated for representative values of ν (0.3, 0.5, 0.7, 0.9) against the white-noise limit ν = 1. We also identify the interval 0.4 ≲ ν ≲ 0.8 where memory-induced changes exceed 20 % at late times, providing a concrete range for physically motivated discussion. While a direct matching to lattice heavy-quark diffusion coefficients or experimental p_T spectra lies outside the scope of this exploratory work, we relate the ν = 1 limit to the standard Langevin parameters used in heavy-ion phenomenology. Error estimates tied to lattice inputs are acknowledged as a future requirement once ν is fixed by an independent QCD calculation. revision: yes

standing simulated objections not resolved

Providing a first-principles QCD derivation or numerical value for the memory parameter ν from lattice gluon correlators or the heavy-quark self-energy is beyond the scope of the present manuscript.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper explicitly frames its work as a phenomenological model study: it adopts a generalized Langevin equation, introduces time-correlated noise via the Caputo fractional derivative of free order ν (chosen to represent memory strength), solves the resulting stochastic equations, and reports the resulting changes in observables relative to the white-noise limit. No step claims a first-principles QCD derivation whose output is then shown to equal the input by construction; the reported influence is simply the direct numerical consequence of the chosen model equations. Because the framework is declared upfront and the calculations are standard solutions within that framework, the derivation chain is self-contained and contains no load-bearing self-definition, fitted-parameter renaming, or self-citation reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on one free parameter (the fractional order nu) and one domain assumption that the generalized Langevin equation with fractional noise captures the essential non-Markovian dynamics of heavy quarks in the QGP; no new particles or forces are postulated.

free parameters (1)

nu
Order of the Caputo fractional derivative that sets the power-law decay of noise correlations; its value is not derived from first-principles QCD and must be chosen or fitted.

axioms (1)

domain assumption The generalized Langevin equation with time-correlated noise generated by a Caputo fractional derivative accurately represents heavy-quark Brownian motion inside the quark-gluon plasma.
Invoked at the outset to justify replacing standard white noise with fractional noise; no derivation from QCD is supplied.

pith-pipeline@v0.9.0 · 5399 in / 1349 out tokens · 104914 ms · 2026-05-10T17:36:20.832169+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

100 extracted references · 65 canonical work pages

[1]

In this case, the drag coefficient in Eq

Purely diffusive motion For illustrative purposes, the one-dimensional (1-D) pure-diffusion condition is taken, although the actual nu- merical calculations are performed in three dimensions of the HQs momentum evolution. In this case, the drag coefficient in Eq. (22) is set to zero, and the initial condi- tion is taken asp(0) = 0, so that the Langevin eq...
[2]

Adams et al

J. Adams et al. (STAR), Phys. Rev. Lett.97, 162301 (2006), arXiv:nucl-ex/0604018

work page arXiv 2006
[3]

Adamset al.(STAR), Nucl

J. Adams et al. (STAR), Nucl. Phys. A757, 102 (2005), arXiv:nucl-ex/0501009

work page arXiv 2005
[4]

Adcoxet al.(PHENIX), Nucl

K. Adcox et al. (PHENIX), Nucl. Phys. A757, 184 (2005), arXiv:nucl-ex/0410003

work page arXiv 2005
[5]

Aamodt et al

K. Aamodt et al. (ALICE), Phys. Rev. Lett.105, 252301 (2010), arXiv:1011.3916 [nucl-ex]

work page arXiv 2010
[6]

Arsene et al

I. Arsene et al. (BRAHMS), Phys. Rev. C72, 014908 (2005), arXiv:nucl-ex/0503010

work page arXiv 2005
[7]

van Hees and R

H. van Hees and R. Rapp, Phys. Rev. C71, 034907 (2005), arXiv:nucl-th/0412015

work page arXiv 2005
[8]

Heavy Quarks in the Quark-Gluon Plasma

R. Rapp and H. van Hees (2010) pp. 111–206, arXiv:0903.1096 [hep-ph]

work page Pith review arXiv 2010
[9]

S. Cao, T. Luo, G.-Y. Qin, and X.-N. Wang, Phys. Rev. C94, 014909 (2016), arXiv:1605.06447 [nucl-th]

work page arXiv 2016
[10]

Cao, G.-Y

S. Cao, G.-Y. Qin, and S. A. Bass, Phys. Rev. C92, 024907 (2015), arXiv:1505.01413 [nucl-th]

work page arXiv 2015
[11]

Scardina, S

F. Scardina, S. K. Das, V. Minissale, S. Plumari, and V. Greco, Physical Review C96, 044905 (2017). 11

2017
[12]

M. He, H. van Hees, and R. Rapp, Prog. Part. Nucl. Phys.130, 104020 (2023), arXiv:2204.09299 [hep-ph]

work page arXiv 2023
[13]

T. Song, H. Berrehrah, D. Cabrera, J. M. Torres- Rincon, L. Tolos, W. Cassing, and E. Bratkovskaya, Phys. Rev. C92, 014910 (2015), arXiv:1503.03039 [nucl- th]

work page arXiv 2015
[14]

Andronicet al., Eur

A. Andronic et al., Eur. Phys. J. C76, 107 (2016), arXiv:1506.03981 [nucl-ex]

work page arXiv 2016
[15]

Dong and V

X. Dong and V. Greco, Prog. Part. Nucl. Phys.104, 97 (2019)

2019
[16]

Heavy-flavor production and medium properties in high-energy nuclear collisions - What next?,

G. Aarts et al., Eur. Phys. J. A53, 93 (2017), arXiv:1612.08032 [nucl-th]

work page arXiv 2017
[17]

Plumari, V

S. Plumari, V. Minissale, S. K. Das, G. Coci, and V. Greco, Eur. Phys. J. C78, 348 (2018), arXiv:1712.00730 [hep-ph]

work page arXiv 2018
[18]

P. B. Gossiaux and J. Aichelin, Phys. Rev. C78, 014904 (2008), arXiv:0802.2525 [hep-ph]

work page arXiv 2008
[19]

Prakash, M

J. Prakash, M. Kurian, S. K. Das, and V. Chandra, Phys. Rev. D103, 094009 (2021), arXiv:2102.07082 [hep-ph]

work page arXiv 2021
[20]

Prakash, V

J. Prakash, V. Chandra, and S. K. Das, Phys. Rev. D 108, 096016 (2023), arXiv:2306.07966 [hep-ph]

work page arXiv 2023
[21]

Prakash and M

J. Prakash and M. Y. Jamal, (2023), arXiv:2304.04003 [nucl-th]

work page arXiv 2023
[22]

M. Y. Jamal, J. Prakash, I. Nilima, and A. Bandyopad- hyay, (2023), arXiv:2304.09851 [hep-ph]

work page arXiv 2023
[23]

Zaccone, Nuclear Physics B1000, 116483 (2024)

A. Zaccone, Nuclear Physics B1000, 116483 (2024)

2024
[24]

Singh, M

M. Singh, M. Kurian, S. Jeon, and C. Gale, Phys. Rev. C108, 054901 (2023), arXiv:2306.09514 [nucl-th]

work page arXiv 2023
[25]

Kurian, M

M. Kurian, M. Singh, V. Chandra, S. Jeon, and C. Gale, Phys. Rev. C102, 044907 (2020), arXiv:2007.07705 [hep-ph]

work page arXiv 2020
[26]

Mazumder, T

S. Mazumder, T. Bhattacharyya, J.-e. Alam, and S. K. Das, Phys. Rev. C84, 044901 (2011), arXiv:1106.2615 [nucl-th]

work page arXiv 2011
[27]

M. Y. Jamal, S. K. Das, and M. Ruggieri, Phys. Rev. D103, 054030 (2021)

2021
[28]

M. Y. Jamal and B. Mohanty, Eur. Phys. J. C81, 616 (2021), arXiv:2101.00164 [nucl-th]

work page arXiv 2021
[29]

M. Y. Jamal and B. Mohanty, Eur. Phys. J. Plus136, 130 (2021), arXiv:2002.09230 [nucl-th]

work page arXiv 2021
[30]

Y. Sun, S. Plumari, and S. K. Das, Phys. Lett. B843, 138043 (2023), arXiv:2304.12792 [nucl-th]

work page arXiv 2023
[31]

Plumari, G

S. Plumari, G. Coci, V. Minissale, S. K. Das, Y. Sun, and V. Greco, Phys. Lett. B805, 135460 (2020), arXiv:1912.09350 [hep-ph]

work page arXiv 2020
[32]

Prakash and M

J. Prakash and M. Y. Jamal, Journal of Physics G: Nu- clear and Particle Physics51, 025101 (2023)

2023
[33]

Du and W

X. Du and W. Qian, arXiv preprint arXiv:2312.16294 (2023)

work page arXiv 2023
[34]

Shaikh, M

A. Shaikh, M. Kurian, S. K. Das, V. Chandra, S. Dash, and B. K. Nandi, Phys. Rev. D104, 034017 (2021), arXiv:2105.14296 [hep-ph]

work page arXiv 2021
[35]

Kumar, M

A. Kumar, M. Kurian, S. K. Das, and V. Chandra, Phys. Rev. C105, 054903 (2022), arXiv:2111.07563 [hep-ph]

work page arXiv 2022
[36]

Parkash, S

Sumit, J. Parkash, S. K. Das, and N. Haque, (2025), arXiv:2506.01922 [hep-ph]

work page arXiv 2025
[37]

Altenkort, O

L. Altenkort, O. Kaczmarek, R. Larsen, S. Mukherjee, P. Petreczky, H.-T. Shu, and S. Stendebach (HotQCD Collaboration), Phys. Rev. Lett.130, 231902 (2023)

2023
[38]

S. K. Das, J. M. Torres-Rincon, and R. Rapp, (2024), arXiv:2406.13286 [hep-ph]

work page arXiv 2024
[39]

Chandra and S

V. Chandra and S. K. Das, Eur. Phys. J. ST233, 429 (2024), arXiv:2402.18870 [hep-ph]

work page arXiv 2024
[40]

Debnath, R

M. Debnath, R. Ghosh, M. Y. Jamal, M. Kurian, and J. Prakash, Phys. Rev. D109, L011503 (2024), arXiv:2311.16005 [hep-ph]

work page arXiv 2024
[41]

M. Y. Jamal, F.-P. Li, L.-G. Pang, and G.-Y. Qin, Phys. Rev. C113, 034915 (2026), arXiv:2509.14970 [hep-ph]

work page arXiv 2026
[42]

S. K. Das et al., Int. J. Mod. Phys. E34, 2544003 (2025), arXiv:2412.14026 [nucl-ex]

work page arXiv 2025
[43]

S. K. Das et al., Int. J. Mod. Phys. E31, 12 (2022), arXiv:2208.13440 [nucl-th]

work page arXiv 2022
[44]

M. L. Sambataro, S. Plumari, S. K. Das, and V. Greco, (2025), arXiv:2510.19448 [hep-ph]

work page arXiv 2025
[45]

S. K. Das, O. Soloveva, T. Song, and E. Bratkovskaya, Phys. Rev. C112, 064901 (2025), arXiv:2507.22620 [nucl-th]

work page arXiv 2025
[46]

D. Dey, A. Bandyopadhyay, S. K. Das, S. Dash, V. Chandra, and B. K. Nandi, Phys. Rev. D112, 016011 (2025), arXiv:2504.02284 [hep-ph]

work page arXiv 2025
[47]

Minissale, S

V. Minissale, S. Plumari, Y. Sun, and V. Greco, Eur. Phys. J. C84, 228 (2024), arXiv:2305.03687 [hep-ph]

work page arXiv 2024
[48]

Oliva, G

L. Oliva, G. Parisi, V. Greco, and M. Ruggieri, Phys. Rev. D112, 014008 (2025), arXiv:2412.07967 [hep-ph]

work page arXiv 2025
[49]

Mazumder, T

S. Mazumder, T. Bhattacharyya, J.-e. Alam, and S. K. Das, Phys. Rev. C84, 044901 (2011)

2011
[50]

Bhattacharyya, E

T. Bhattacharyya, E. Megias, and A. Deppman, Phys. Lett. B856, 138907 (2024), arXiv:2405.15679 [hep-ph]

work page arXiv 2024
[51]

Young, B

C. Young, B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C86, 034905 (2012)

2012
[52]

T. Lang, H. van Hees, G. Inghirami, J. Steinheimer, and M. Bleicher, Phys. Rev. C93, 014901 (2016)

2016
[53]

Cao and S

S. Cao and S. A. Bass, Phys. Rev. C84, 064902 (2011)

2011
[54]

Nonperturbative Heavy-Quark Diffusion in the Quark-Gluon Plasma

H. van Hees, M. Mannarelli, V. Greco, and R. Rapp, Phys. Rev. Lett.100, 192301 (2008), arXiv:0709.2884 [hep-ph]

work page Pith review arXiv 2008
[55]

Caoet al., Phys

S. Cao et al., Phys. Rev. C99, 054907 (2019), arXiv:1809.07894 [nucl-th]

work page arXiv 2019
[56]

Beraudoet al., Nucl

A. Beraudo et al., Nucl. Phys. A979, 21 (2018), arXiv:1803.03824 [nucl-th]

work page arXiv 2018
[57]

Open Heavy Flavor in QCD Matter and in Nuclear Collisions

F. Prino and R. Rapp, J. Phys. G43, 093002 (2016), arXiv:1603.00529 [nucl-ex]

work page Pith review arXiv 2016
[58]

M. He, H. van Hees, P. B. Gossiaux, R. J. Fries, and R. Rapp, Phys. Rev. E88, 032138 (2013), arXiv:1305.1425 [nucl-th]

work page arXiv 2013
[59]

Xuet al., Phys

Y. Xu et al., Phys. Rev. C99, 014902 (2019), arXiv:1809.10734 [nucl-th]

work page arXiv 2019
[60]

M. He, R. J. Fries, and R. Rapp, Phys. Rev. Lett.110, 112301 (2013), arXiv:1204.4442 [nucl-th]

work page arXiv 2013
[62]

Zhang, L

C. Zhang, L. Zheng, S. Shi, and Z.-W. Lin, Phys. Lett. B846, 138219 (2023), arXiv:2210.07767 [nucl-th]

work page arXiv 2023
[63]

Schenke and C

B. Schenke and C. Greiner, Phys. Rev. Lett.98, 022301 (2007)

2007
[64]

J. I. Kapusta, B. M¨ uller, and M. Stephanov, Phys. Rev. C85, 054906 (2012)

2012
[65]

Ruggieri, M

M. Ruggieri, M. Frasca, and S. K. Das, Chin. Phys. C 43, 094105 (2019), arXiv:1903.11302 [nucl-th]

work page arXiv 2019
[66]

Sch¨ uller, A

B. Sch¨ uller, A. Meistrenko, H. Van Hees, Z. Xu, and C. Greiner, Annals Phys.412, 168045 (2020), arXiv:1905.09652 [cond-mat.stat-mech]

work page arXiv 2020
[67]

W. Chen, C. Greiner, and Z. Xu, Phys. Rev. E107, 064131 (2023)

2023
[68]

Greiner, K

C. Greiner, K. Wagner, and P.-G. Reinhard, Phys. Rev. C49, 1693 (1994). 12

1994
[69]

A. E. Gegechkori, Y. A. Anischenko, P. N. Nadtochy, and G. D. Adeev, Phys. Atom. Nucl.71, 2007 (2008)

2007
[70]

F. A. Ivanyuk, S. V. Radionov, C. Ishizuka, and S. Chiba, (2021), arXiv:2103.14145 [nucl-th]

work page arXiv 2021
[71]

J. I. Kapusta and C. Young, Phys. Rev. C90, 044902 (2014), arXiv:1404.4894 [nucl-th]

work page arXiv 2014
[72]

Murase and T

K. Murase and T. Hirano, (2013), arXiv:1304.3243 [nucl-th]

work page arXiv 2013
[73]

Hammelmann, J

J. Hammelmann, J. M. Torres-Rincon, J.-B. Rose, M. Greif, and H. Elfner, Phys. Rev. D99, 076015 (2019), arXiv:1810.12527 [hep-ph]

work page arXiv 2019
[74]

Ruggieri, Pooja, J

M. Ruggieri, Pooja, J. Prakash, and S. K. Das, Phys. Rev. D106, 034032 (2022), arXiv:2203.06712 [hep-ph]

work page arXiv 2022
[75]

Pooja, S. K. Das, V. Greco, and M. Ruggieri, Phys. Rev. D108, 054026 (2023), arXiv:2306.13749 [hep-ph]

work page arXiv 2023
[76]

P. Guo, C. Zeng, C. Li, and Y. Chen, Fractional Cal- culus and Applied Analysis16, 123 (2013)

2013
[77]

Li and F

C. Li and F. Zeng, Numerical Functional Analysis and Optimization34, 149 (2013)

2013
[78]

K. S. Miller and B. Ross, John Wiley & Sons, Inc., New York , xvi+366 (1993)

1993
[79]

Caputo and F

M. Caputo and F. Mainardi, Rivista del Nuovo Cimento 1, 161 (1971)

1971
[80]

Carpinteri and F

A. Carpinteri and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics378(2014)

2014
[81]

Ciesielski and J

M. Ciesielski and J. Leszczyski, The European Physical Journal B36, 33 (2003)

2003

Showing first 80 references.