Traitement amélioré de la description théorique de la dynamique des quarkonia dans le plasma quarks-gluons : de l'approximation semi-classique aux équations maîtresses quantiques unifiées entre le régime brownien quantique et le régime optique quanti

Heavy quarkonia are one of the probes of Quark-Gluon Plasma (QGP) formed in Ultra-Relativistic Heavy-Ion collisions (URHIC). Over the past decade, there has been an increasing interest in the use of open quantum systems (OQS) formalism in the study of the in- QGP quarkonia dynamics. In particular, it has been shown that the Lindblad equation can result in semiclassical equations, which have been previously employed by several phenomenological models. In the first part of this thesis, we investigate the validity of the semiclassical approximation, and its ability to describe certain non-trivial quantum effects and reach the appropriate thermal limit. The second part of the thesis aims to address some theoretical challenges associated with the use of the OQS formalism in the study of in-QGP quarkonia dynamics. In particular, due to the dynamical aspect of the QGP and its time-dependent temperature, the dynamics of in- QGP quarkonia covers two different regimes of the OQS formalism, which are described by two different master equations, namely, the quantum Brownian and optical regimes. We first explore the transition between the two regimes and elucidate the link between their respective master equations. Secondly, in order to describe the complete in-QGP quarkonia time evolution with a single master equation, we apply the universal Lindblad equation (ULE) to the QGP-quarkonia system and derive a set of coupled singlet-octet universal equations.