Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma

TL;DR

This paper develops equations describing the quantum and classical evolution of heavy quarks in a quark-gluon plasma, incorporating approximations to connect with known results and proposing numerical strategies for quark-antiquark pairs.

Contribution

It introduces a framework for modeling heavy quark dynamics in QGP using reduced density matrices and explores two numerical solution methods.

Findings

Derived equations for heavy quark evolution in QGP.

Connected quantum and classical descriptions via approximations.

Proposed Langevin and Boltzmann-based numerical methods.

Abstract

We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate strategies to solve numerically the resulting equations in the case of a quark-antiquark pair. One involves Langevin equations with additional random color forces, the other treats the transition between the singlet and octet color configurations as collisions in a Boltzmann equation which can be solved with Monte Carlo techniques.