Heavy-quark thermalization in the quark-gluon plasma via a fractional Langevin equation
Abstract
The dynamics of heavy quarks in the quark-gluon plasma is commonly described within a standard Langevin equation framework. In this work, we extend the conventional framework by using a fractional Langevin equation based on the Caputo derivative of order α with 1<α≤ 2. We solve the fractional Langevin equation and derive the corresponding {\textit {fractional fluctuation-dissipation theorem}} for the heavy quark thermalization in the quark-gluon plasma medium. We calculate the time evolution of the mean-squared momentum, mean-squared displacement, momentum distribution, energy loss, longitudinal momentum loss, transverse momentum broadening, and the nuclear suppression factor of the heavy quarks. The mean-squared momentum thermalizes to the same value for all α at late times, in agreement with the fractional fluctuation-dissipation theorem, and the nuclear suppression factor shows a systematic α-dependence. The energy loss of an energetic heavy quark grows strongly with α. The time evolution of the heavy quark momentum distribution provides additional sensitivity to the fractional dynamics of the heavy quarks in the QGP medium.
Related
- Entropy Production and Thermalization in Heavy-Quark Langevin Dynamics
- Heavy quark thermalization using phonon-heavy quark EFT
- Hot and dense QCD equation of state from the complex Langevin equation
- Equation of state of hot and dense QCD using the complex Langevin equation
- Beyond Rough Volatility: Decoupling Memory and Scaling via a Generalized Langevin Equation
BibTeX
@misc{prakash2026heavyquark,
title = {{Heavy-quark thermalization in the quark-gluon plasma via a fractional Langevin equation}},
author = {Jai Prakash and Mohammad Yousuf Jamal and Shanshan Cao and Guang-You Qin and Yifeng Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26086},
eprint = {2610.26086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26086},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Heavy-quark thermalization in the quark-gluon plasma via a fractional Langevin equation
AU - Jai Prakash
AU - Mohammad Yousuf Jamal
AU - Shanshan Cao
AU - Guang-You Qin
AU - Yifeng Sun
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.26086
UR - https://arxiv.org/abs/2610.26086
AB - The dynamics of heavy quarks in the quark-gluon plasma is commonly described within a standard Langevin equation framework. In this work, we extend the conventional framework by using a fractional Langevin equation based on the Caputo derivative of order α with 1<α≤ 2. We solve the fractional Langevin equation and derive the corresponding {\textit {fractional fluctuation-dissipation theorem}} for the heavy quark thermalization in the quark-gluon plasma medium. We calculate the time evolution of the mean-squared momentum, mean-squared displacement, momentum distribution, energy loss, longitudinal momentum loss, transverse momentum broadening, and the nuclear suppression factor of the heavy quarks. The mean-squared momentum thermalizes to the same value for all α at late times, in agreement with the fractional fluctuation-dissipation theorem, and the nuclear suppression factor shows a systematic α-dependence. The energy loss of an energetic heavy quark grows strongly with α. The time evolution of the heavy quark momentum distribution provides additional sensitivity to the fractional dynamics of the heavy quarks in the QGP medium.
ER -