Real-time quantum dynamics of heavy quark systems at high temperature

TL;DR

This paper develops a unified real-time quantum dynamical framework for heavy quark systems at high temperature, enabling the study of both single quarks and quarkonia using non-equilibrium quantum field theory.

Contribution

It introduces a method based on the closed-time path formalism that describes heavy quark propagation and bound states within a single operator framework, incorporating perturbation theory and stochastic equations.

Findings

Reproduces perturbative results for drag force and complex potential.

Derives master equations for quantum Brownian motion and correlators.

Provides stochastic wave function evolution equations.

Abstract

On the basis of the closed-time path formalism of non-equilibrium quantum field theory, we derive the real-time quantum dynamics of heavy quark systems. Even though our primary goal is the description of heavy quarkonia, our method allows a unified description of the propagation of single heavy quarks as well as their bound states. To make calculations tractable, we deploy leading-order perturbation theory and consider the non-relativistic limit. Various dynamical equations, such as the master equation for quantum Brownian motion and time-evolution equation for heavy quark and quarkonium forward correlators, are obtained from a single operator, the renormalized effective Hamiltonian. We are thus able to reproduce previous results of perturbative calculations of the drag force and the complex potential simultaneously. In addition, we present stochastic time-evolution equations for heavy quark and quarkonium wave function, which are equivalent to the dynamical equations.