Quantum vs. semiclassical description of in-QGP quarkonia in the quantum Brownian regime

TL;DR

This work tests the validity of the semiclassical approximation to the quantum master equation for a charmonium pair in a quark–gluon plasma within the quantum Brownian regime. By comparing the Lindblad-based quantum evolution of the 1D abelian system to its semiclassical Fokker–Planck counterpart across temperatures and initial states, the authors quantify the agreement using Wigner densities and a distance measure, finding that the semiclassical description reproduces quantum results with about 10% accuracy for quarkonia yields. The rapid decoherence induced by the bath drives classicalization, reducing quantum interferences and enabling efficient semiclassical modeling, though the Lindblad dynamics do not exactly thermalize to Gibbs–Boltzmann states, especially at late times when the L4 term contributes. The study supports using semiclassical transport for charmonium phenomenology in heavy-ion collisions and points to future work extending the analysis to non-abelian QCD, QOR perspectives, and higher-dimensional dynamics.

Abstract

In this work, we explore the range of validity of the semiclassical approximation of a quantum master equation designed to describe the $c\bar{c}$ dynamics in a quark gluon plasma at various temperatures, in the quantum Brownian regime. We perform a comparative study of various properties, e.g. the charmonia yield, of the Wigner density obtained with the Lindblad equation and with the associated semiclassical Fokker-Planck equation. The semiclassical description is found to reproduce with a remarkable accuracy the results obtained through the full quantum description. We show that, to a large extent, this can be attributed to the non-unitary components of the dynamics that result from the contact of the $c\bar{c}$ subsystem with the thermal bath, leading to a rapid classicalization of the subsystem.

Figures (17)

• Figure 1: QM vs SC time evolution of the Wigner distribution $\mathcal{D}(r,p)$ for relative distance $r$ and momentum $p$ resulting from the evolution of a 1S initial state in a QGP at $T=0.3$ GeV. For the quantum case, we show the evolution both with (left column) or without (middle column) the $\mathcal{L}_4$ term.
• Figure 2: QM vs SC time evolution of root mean squared momentum for various QGP temperatures (the lower edges of the QM bands correspond to the calculation without $\mathcal{L}_4$). The horizontal lines refer to the stationary values expected from Gibbs-Boltzmann distribution, i.e. $\sqrt{\langle p^2\rangle}(t=\infty)=\sqrt{MT/2}$.
• Figure 3: QM vs SC time evolution of root mean squared radius for various QGP temperatures. The horizontal lines refer to the stationary values expected from Gibbs-Boltzmann distribution. These indeed depend on the temperature since the density is more localized toward small $r$ for low temperature, due to the attractive potential.
• Figure 4: Left: The time evolution of the negativity indicator $\delta(t)$ for the case a quantum dynamics with $\mathcal{L}_4$ included in the dynamics. Right: the corresponding Wigner distribution at $t=20\,{\rm fm}/c$ for $T=0.2$ GeV. Small negative values can be detected at very small $r$ and large $p$.
• Figure 5: Time evolution of the root mean squared $\sqrt{\langle y^2\rangle}$ (thick curves), compared to $y_\mathrm{infl}$, the inflection point of the imaginary potential (thin horizontal lines, corresponding, from top to bottom, to $T$=0.2, 0.3, 0.4 and 0.6, in GeV).