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arXiv:2111.15402 · EPJ Web of Conferences

Nonequilibrium evolution of quarkonium in medium

Yukinao Akamatsu, Takahiro Miura

Published Jan 1, 2022• 5 citations
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Abstract

We review recent progress in open quantum system approach to the description of quarkonium in the quark-gluon plasma. A particular emphasis is put on the Lindblad equations for quarkonium and its numerical simulations.
DOI
10.1051/epjconf/202225801006

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Accurate modelling and understanding of quarkonium production in ultrarelativistic heavy ion collisions requires a formalism that preserves the quantum properties of microscopic QˉQ\bar{Q}QQˉ​Q systems while treating the interaction of such pairs with the quark-gluon plasma (QGP). The open quantum system approach has recently emerged as one of the most fruitful schemes to meet such requirements. However, the quantum master equations obtained so far in this context are derived assuming a strict ordering between the QGP temperature TTT and the QˉQ\bar{Q}QQˉ​Q energy gaps (ΔEΔEΔE) of the quarkonia bound states. This limits their predictive power since, as the QGP expands and cools down, the system traverse all regimes between the quantum Brownian motion (QBM) regime for T≳ΔET\gtrsim ΔET≳ΔE to the quantum optical (QO) regime for ΔE≳TΔE\gtrsim TΔE≳T. In this paper, we derive and present a more general non-abelian quantum master equation of the Lindblad type, which does not suffer from these limitations and thus allows to faithfully describe the quantum evolution of the QQˉQ\bar{Q}QQˉ​ pairs during the whole QGP-evolution. We also provide some illustration of the key quantities governing this equation.
\nIn recent years, a significant theoretical effort has been made towards a dynamical description of quarkonia inside the Quark-Gluon Plasma (QGP), using the open quantum systems formalism. In this framework, one can get a real-time description of a quantum system (here the quarkonium) in interaction with a thermal bath (the QGP) by integrating out the bath degrees of freedom and studying the system reduced density matrix. We investigate the real-time dynamics of a correlated heavy quark-antiquark pair inside the QGP using a quantum master equation previously derived from first QCD principles in [4]. The full equation is directly resolved in 1D to lessen computing costs and is used for the first time to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution.\n
I review recent applications of the open quantum system framework in the understanding of quarkonium suppression in heavy-ion collisions, which has been used as a probe of the quark–gluon plasma for decades. The derivation of the Lindblad equations for quarkonium in both the quantum Brownian motion and the quantum optical limits and their semiclassical counterparts is explained. The hierarchy of time scales assumed in the derivation is justified from the separation of energy scales in nonrelativistic effective field theories of QCD. Physical implications of the open quantum system approach are also discussed. Finally, I list some open questions for future studies.
Description théorique de la dynamique des quarkonia dans le plasma de quarks et de gluons au moyen d'une approche de type équation maîtresse quantique La Chromodynamique Quantique (QCD) prédit l'existence d'un état de la matière appelé Plasma de Quarks et de Gluons (PQG) dans des conditions extrêmes de température et de pression, qui peut être produit lors de collisions d'ions lourds. Une observable du PQG est la suppression des quarkonia (états liés de quark-antiquark lourds), qui est définie par une plus faible production de ces états en présence de PQG par rapport à la production en l'absence de plasma.Ces dernières années, un effort significatif a été réalisé d'un point de vue théorique vers une description dynamique des quarkonia au sein du Plasma de Quarks et de Gluons, à l'aide du formalisme des systèmes quantiques ouverts. Dans ce cadre, il est possible d'obtenir une description en temps réel d'un système quantique (ici un quarkonium) en interaction avec un bain thermique (le PQG) en étudiant la matrice densité réduite du système.Cette thèse étudie la dynamique d'états quarkonium en résolvant une équation maîtresse quantique basée sur l'approche de Blaizot & Escobedo. Plus précisément, cette équation est résolue numériquement directement pour la première fois dans le cas d'un PQG statique et dans le cas d'un PQG se refroidissant. Les populations d'états quarkonium sont étudiées et la validité d'approximations semi-classiques amenant à des équations de Langevin est examinée.
In recent years, a significant theoretical effort has been made towards a dynamical description of quarkonia inside the Quark-Gluon Plasma (QGP), using the open quantum systems formalism. In this framework, one can get a real-time description of a quantum system (here the quarkonium) in interaction with a thermal bath (the QGP) by integrating out the bath degrees of freedom and studying the system reduced density matrix. We investigate the real-time dynamics of a correlated heavy quark-antiquark pair inside the QGP using a quantum master equation previously derived from first QCD principles in [4]. The full equation is directly resolved in 1D to lessen computing costs and is used for the first time to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution.
We study the properties of the Lindbladian quantum mechanical evolution of quarkonia with non-Abelian charges (color-singlet and octet) in the quark-gluon plasma. We confirm that heavy quark recoils in the Lindblad equation correctly thermalize quarkonium colorful states within statistical errors from the simulation method. We also demonstrate that the Lindblad equation in the dipole limit can provide an efficient alternative method, which is applicable to a finite time evolution before thermalization and dramatically reduces the numerical cost. Our findings will serve as a foundation for large-scale simulation of quarkonium dynamics in the relativistic heavy-ion collisions.