# Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma

## TL;DR

This paper develops a quantum master equation approach to study how dissipation influences the real-time evolution and thermalization of heavy quarkonium in the quark-gluon plasma, linking QCD to phenomenological models.

## Contribution

It introduces a novel non-equilibrium master equation derived from quantum field theory for quarkonium dynamics in QGP, connecting QCD with non-linear Schrödinger models.

## Key findings

- Dissipative effects enable quarkonium to thermalize within QGP lifetime.
- The quantum evolution can be represented as a stochastic non-linear Schrödinger equation.
- Dissipation impacts quarkonium dynamics at early stages in heavy ion collisions.

## Abstract

In this paper we study the real-time evolution of heavy quarkonium in the quark-gluon plasma (QGP) on the basis of the open quantum systems approach. In particular, we shed light on how quantum dissipation affects the dynamics of the relative motion of the quarkonium state over time. To this end we present a novel non-equilibrium master equation for the relative motion of quarkonium in a medium, starting from Lindblad operators derived systematically from quantum field theory. In order to implement the corresponding dynamics, we deploy the well established quantum state diffusion method. In turn we reveal how the full quantum evolution can be cast in the form of a stochastic non-linear Schr\"odinger equation. This for the first time provides a direct link from quantum chromodynamics (QCD) to phenomenological models based on non-linear Schr\"odinger equations. Proof of principle simulations in one-dimension show that dissipative effects indeed allow the relative motion of the constituent quarks in a quarkonium at rest to thermalize. Dissipation turns out to be relevant already at early times well within the QGP lifetime in relativistic heavy ion collisions.